Research ArticleComplexity Analysis of a Four-DimensionalEnergy-Economy-Environment Dynamic System

Shuai Jin1 and Liuwei Zhao 12

1School of Management Jiangsu University Zhenjiang Jiangsu 212013 China2School of Business Jiangsu University of Technology Changzhou Jiangsu 213001 China

Correspondence should be addressed to Liuwei Zhao 136901672qqcom

Received 16 June 2020 Revised 7 August 2020 Accepted 11 August 2020 Published 27 August 2020

Academic Editor Viorel-Puiu Paun

Copyright copy 2020 Shuai Jin and Liuwei Zhao -is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A novel four-dimensional energy economic and environmental (3E) under energy reduction constraints chaotic system is proposed-e acquisition of environmental quality data is the key to this paper During the course of the study we used Bayesian estimationalgorithm to calibrate the environmental quality Based on the official data the LevenbergndashMarquardt backpropagation neural networkmethod was optimized by genetic algorithm to effectively identify the parameters in the 3E system -e research results show thatalthough increasing energy reduction inputs can improve environmental quality the effect on energy intensity and overall stability of thesystem is not obvious When polluting input in the ecological environment system affects its maximum capacity the environmentalsystem collapses (ie the ecological system can no longer purify the environment through the self-circulation process and will eventuallydie out) -erefore it is necessary to correctly grasp the ecological environment protection and the relationship between economicdevelopments and explore synergies to promote ecological priorities and green development new ideas

1 Introduction

In the context of the rapid development of the globaleconomy China has become one of the largest economygroups however there are obvious contradictions betweenrapid economic growth with energy use and the protectionof the environment -ere are mutual influences and mutualchecks and balances among energy systems economicsystems and environmental systems -erefore to achievecoordinated development of energy economic and envi-ronmental system has become an important part ofachieving development goals of the region Economy-en-ergy-environment system has come into being 3E systemwhich is used for analyzing the comprehensive developmentlevel of economy energy and environment for a region thususing the result data to judge the degree of coordinationamong economy energy and environment and make a newplan

New elements have been continuously created as theevolution of 3E systems has not followed the linear mech-anism which has made the world even more diversified and

complicated -us it is fair to say that the nonlinear evo-lution model has become the prerequisite that has graduallyenriched and complicated the 3E system It is the new el-ements coming from the nonlinear mechanism that hassupported the evolution and complicated the elementsAccordingly the information that follows suits has con-tinued to increase and accumulate which has ensured thesustainable development -e complicated nonlinearmechanism generally lies in the elements outside and insideof the environment system which has stabilized thestructure organization and the conditioning mechanism forthe system to stimulate and confine the revolution of thewhole system

Presently we have seen massive research on nonlinearmodelrsquos complexity For instance Zhao et al believe thatthere are many species in the environmental system thereare complex relationships among species such as parasitismsymbiosis and natural enemies -ere are direct or indirectconnections among all species which constitute a complexecological network Because the environmental system hasthe characteristics of nonlinearity self-organization

HindawiComplexityVolume 2020 Article ID 7626792 14 pageshttpsdoiorg10115520207626792

nonnegotiability dynamics openness multilevel self-sim-ilarity and so on it is a typical complex system and it is alarge system with many elements levels and complex re-lationships If we want to solve the current environmentalproblems facing mankind we must apply complexity theoryto environmental problems making the structure of envi-ronmental system more reasonable and the balance of en-vironment economy and society rebuilt [1] Fang believesthat structural complexity is one of the most fundamentalproblems of dynamic complexity of ecosystems -e de-velopment and application of dynamic system theory arehelpful to understand the complexity of ecosystem It ispointed out that structural complexity and dynamic com-plexity are interrelated Simple dynamic models of ecosys-tem show that simple structural systems can produce verycomplex and unpredictable dynamic behavior in some casesHowever the ecosystems with complex structures may notnecessarily produce complex dynamic behaviors [2] De-velopment and application of the dynamics system wouldhelp enhance the understanding of 3E systemrsquos complexity-e research would also help indicate that complexity be-tween structure and dynamics are interrelated -e 3Esystemrsquos simple dynamic model indicated that simplestructure system would generate complicated and unpre-dictable dynamic behavior However the complied eco-system would not necessarily lead to complicated dynamicbehavior [3] We can make basic judgment on current re-searches on 3E systemrsquos internal connectivity and interactionfrommultiple perspectives Some of the researches are basedon the samples from the time series and applied fromcointegration and causal tests discussing the relationshipbetween energy and economy Scholars all around the worldhave consensus about the interaction of the two believingthat consumption of energy and economic growth has beenhighly correlated for the long time and yet exhibits notableregional difference [4 5] Regarding the relationship be-tween energy and environment some scholars believe thatincrease in energy output and consumption are the mainculprit behind the degradation of environment [6 7] It isworth noting that most of the researches on the topic arebased on Kuznets curve while the conclusions that followsuit are divergent On the one hand the supporters aim tofigure out the internal motivations [8ndash10] that form the EKCfrom the perspective of economic growth trade and poli-cies -ey have come to the roughly similar conclusion thequality of environment would be improved in tandem witheconomic development following its degradation On theother hand the skeptics of the EKC believe that the rela-tionship between economy and environment could includeU-shape N-shape or synchronous curves [11ndash13]

Some other researches are based on the comprehensivediscussion regarding the 3E system However the scholarshave chosen different research timing and methods mainlyincluding measurement and evaluation of the 3E systemrsquoscoordination [14] application of dynamic CGE model [15]the endogenous growth model [16] and the relationshipsand correlations among outputs of 3E based on the analysisof the econometric model [17] Current literature has basicconsensus of the conclusion regarding the coordination

analysis of the 3E system believing that Chinarsquos coordina-tion remains at a lower level Meanwhile Wei et al haveincluded demographic system into their researches leadingto a dynamically open yet more complicated system in orderto build up multipurpose planning and an integrated modelreflecting a check-and-balance relationship [18] -e re-search comes with a novel angel

Currently environmental protection still falls behind socialand economic development Pollutions caused by multistagesmultifields and multitypes have been continually mountingyet the environmental carrying capacity has (nearly) reached itslimit Hence the worsening environmental problems have notbeen radically resolved In the process of handling the issuespeople have been gradually aware that improvement of theenvironmental quality hinges on well-managed resources re-solved environmental problems and control of pollutantsrsquoemission Good environmental quality is related to the sus-tainable development of the economy and society It is animportant breakthrough to adjust the economic structure andachieve economic growth It is conducive to promoting eco-nomic competition and promoting the development of greendevelopment and environmental industries Accordinglyvarious scholars have embarked on research on energy re-duction For instance Loschel and Otto have built up a dy-namic balance model to study the relationships among thevariables including carbon dioxide emission energy con-sumption speed of technological innovation and economicdevelopment His conclusion suggests that decision-makersprudently design the carbon dioxide emission cut policies [19]Erdmenger and his team detailed the measures for Germany toreach its CO2 emission target by 40 and carbon emission cutby 224 mnMT [20] Xu and his team adopt the AIM and CGEmodels to evaluate sulfur dioxide controlrsquos impact on thepollutant and CO2 emission cut locally-ey believe that Chinacould enjoy the benefits from carbon emission via control oversulfur dioxide emission [21] Cullende and Allood foundthrough research that efficiency is a very important role incarbon emission reduction -e scale of the energy flow is animportant indicator to evaluate potential return from the ef-ficiency Estimating the global energy flowrsquos scale and com-plexity could bring about the maximum energy efficiencyreturn [22] Prasad studied the impact of renewable energypolicies in 39 states on CO2 reduction -ey discovered thatafter 19 statesrsquo introduction of Fund for the Public Interest orsomething similar to ldquocarbon taxrdquo CO2 emission has seennotable and stable decline [23] Fang established a three-di-mensional system for energy conservation and emission re-duction and obtained energy-saving attractions Meanwhilethey evaluate the performance of energy saving and emissioncut [24ndash27] more research is needed [28 29]

In recent years BP neural network has attracted more andmore attention in the field of artificial intelligence Manynonlinear methods have been proposed to predict the trend ofenergy and economy such as BP neural network [30ndash34] BPneural network has unique advantages in economic fields suchas economic analysis [35ndash38] and time series prediction If thecomputation amount allows any number of many-to-manymappings can be fitted with a smaller fitting error -e strongcoupling relationship among the factors in the prediction system

2 Complexity

is an interwoven and interactive relationship which can beexpressed by the connection weights and thresholds betweennodes in each layer Compared with the traditional multipleregression prediction method this expression has better fittingability and precision BP neural network has strong nonlinearfunction approximation ability and has been widely used in timeseries analysis and financial forecasting BP neural network hasthe ability to fit the function and determine the weights andthresholds between neurons through learning process [39]-erefore we depended on the official statistics and measureddata of the China Statistical Yearbook to predict the future trendof 3E

In the process of enhancing environment governance wehave seenmore complicated environmental issues for which it ismore difficult to find solutions With that we see even moredifficulties and complexity for the various projects to furtherstrengthen environment governance and environmental qualityimprovement Presently industrialization urbanization andmodernization have propelled energy demand at a growth stageOngoing consumption increase in fossil fuels with high pollutionand high carbon emission has impeded the sustainable devel-opment for the environment -erefore we need to fully realizethe dynamic complexity of the 3E system and the lag of en-vironmental protection in order to reduce the damage moreeffectively and rationally to the ecological environment systemand make the economy sustainable

With the rapid development of environmental protec-tion the gradual improvement of social-environmentalawareness and the increasing competition in the industrythe environmental governance network is a complexadaptive system formed by the game and interest coordi-nation and self-organization under the market operationmechanism -erefore the research on 3E systems needs topay more attention to the complexity brought by multi-system interaction In general 3E is increasingly showing thedynamic complexity of the system -erefore it is necessaryto study how the three systems of the main body establish aneffective coordination strategy mechanism and study theenvironmental governance network and economy based onsuch microbehavior and game characteristics Develop amacrointegrated structure and a mechanism for the for-mation of good performance in particular the emergence ofthe overall structure and performance of 3E systems and thesystematic analysis between environmental and economicsystems In the meantime judging from the current researchthat concerns the impact of environmental governance andenvironmental governance system engineering and divingdeeply into current study we believe that the followingaspects need to be enhanced and perfected Study the fol-lowing issues First based on the research foundation of therelationship of the dual systems we need to integrate the 3Einto the system analysis by developing theoretical analysesbased on the multiple systemsrsquo coordination and develop-ment angles Secondly we need to study the evaluationpattern of the 3Ersquos complexity -irdly the official data areused to identify the 3E system parameters and the evolutionof the 3E system analyzed It is under such current situationthat the 3E systemrsquos variation pattern would be of signifi-cance to the systemrsquos sustainable development

-is study makes a series of significant contributions tothe research of the 3Ersquos complexity

First this study considers the inclusion of energy re-duction constraints on the 3E system proposed and gets anew four-dimensional system which is more in line withthe actual situation and the current development needsSecond this study deviates from the leading research onenergy-economy-environment systems research that fo-cuses primarily on environmental impact analysis [40]global environmental development [41] eco-industrialsystems planning [42 43] dynamic assessment of urbaneconomy-resource-environment systems [44] and eco-nomic and environmentally sustainable development[45] Here through the stability analysis of dynamic 3Esystem by system complexity theory the gap in meth-odology commonly used in 3E system research is bridged-e results provide a practical policy prescription foreffective pollution control-ird based on the official data the Levenberg-Mar-quardt backpropagation neural network method wasoptimized by genetic algorithm to effectively identifythe parameters in the 3E system which is more con-ducive to better research on the interaction betweenvarious elements of the 3E system

-is paper is organized as follows In Section 2 we con-struct a 3E system with energy-constrained constraints andtheoretically analyze the system through the theory of com-plexity and use numerical simulation to demonstrate thevarious dynamic behaviors of the four-dimensional system InSection 3 the genetic algorithm is used to optimize the LM-BPneural network method to identify and confirm the systemparameters of the four-dimensional system In Section 4 an in-depth analysis of the changes in key parameters of the system iscarried out to study the stability and dynamic complexity of thesystem Finally the main conclusions of this study are given

2 Model Construct and Theoretical Analysis

21ModelConstruct In the paper we consider the inclusionof energy reduction constraints on the 3E system proposedby Zhao et al [1] and get a new four-dimensional systemwhich is more in line with the actual situation and thecurrent development needs Energy economy and envi-ronment (3E) system containing energy reduction con-straints is given in the following form

_x a1xy

M minus 11113874 1113875 minus a2y + a3z + a4w

_y minus b1x + b2y1 minus y

F1113874 1113875 + b3z

1 minus z

E1113874 1113875 minus b4w

_z c1xx

N minus 11113874 1113875 minus c2y minus c3z minus c4w

_w d1x minus d2y + d3z1 minus z

H1113874 1113875 + d4w

y

P minus 11113874 1113875

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

Complexity 3

where x(t) y(t) z(t) are w(t) respectively the level ofenergy conservation and emission reduction pollutionemission economic growth (GDP) and environmentalquality in period t ai bi ci di (i 1 2 3 4) M F E N Hand P are normal numbers t isin I and I is an economic cycle(Table 1)

In system (1) _x represents the change level of energysaving and emission reduction in t period _y represents thelevel of change in pollution emissions in t period _z rep-resents the growth level of economic growth in the t period_w represents the change level of environmental quality in t

period When the impact of pollution exceeds the maximumcapacity of the ecological environment (that _wgt 0) it meansthat the ecological environment is deteriorating In this casethe ecosystem cannot rely on self-regulation to repair-erefore when this situation continues the ecologicalenvironment will eventually be sold out when _wle 0 itmeans that the environmental quality has reached a dynamicbalance or gradually improved and only under this con-dition can the ecological environment be the basis of humansocial development [46ndash48]

By system (1) energy intensity can be launched the formof energy intensity is as follows

energy intensity A economic cycle energy consumption

GDPwithin an economic cycle

(2)

Next we will analyze the dynamics of 3E system con-taining energy reduction constraints By calculation theJacobian matrix of the system (1) can be obtained as follows

J

y

Mminus 11113874 1113875a1

xa1

Mminus a2 a3 a4

minus b1(F minus 2y)b2

F

(E minus 2z)b3

Eminus b4

minus(N minus 2x)c1

Nminus c2 minus c3 minus c4

d1 minus d2 +wd4

P

(H minus 2z)d3

H

y

P minus 1minus 11113874 1113875d4

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)

-e six real equilibrium points of the 3E system (1) arerespectively O(0 0 0 0) S1(x1 y1 z1 w1)S2(x2 y2 z2 w2) S3(x3 y3 z3 w3) S4(x4 y4 z4 w4) andS5(x5 y5 z5 w5) -e Jacobian matrix of system (1) atequilibrium point O(0 0 0 0) is of the following form

J0

minus a1 minus a2 a3 a4

minus b1 b2 b3 minus b4

minus c1 minus c2 minus c3 minus c4

d1 minus d2 d3 minus d4

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

So the characteristic polynomial of J(O) is as follows

f(λ) λ4 + Aλ3 + Bλ2 + Cλ + D 0 (5)

where

A a1 minus b2 + c3 + d4

B a3c1 minus a2b1 + b3c2 minus b2c3 minus a4d1 + b4d2 + c4d3 minus b2d4 + c3d4 + a1 c3 + d4 minus b2( 1113857

C a1b3c2 minus a1b2c3 + a4b2d1 minus a4c3d1 minus a4b1d2 + a1b4d2 + b4c3d2 minus b3c4d2

+ a4c1d3 + b4c2d3 + a1c4d3 minus b2c4d3 minus a1b2d4 + b3c2d4 + a1c3d4 minus b2c3d4

+ a3 c4d1 + c1d4 minus b2c1 minus b1c2( 1113857 minus a2 b3c1 minus b4d1 + b1 c3 + d4( 1113857( 1113857

D a2b4c3d1 minus a2b3c4d1 + a1b4c3d2 minus a1b3c4d2 minus a2b4c1d3 + a1b4c2d3 minus a2b1c4d3 minus a1b2c4d3

minus a4 b3c2d1 minus b2c3d1 + b3c1d2 + b1c3d2 + b2c1d3 + b1c2d3( 1113857 minus a2b3c1d4 + a1b3c2d4

minus a2b1c3d4 minus a1b2c3d4 + a3 b4c2d1 minus b2c4d1 + b4c1d2 + b1c4d2 minus b2c1d4 minus b1c2d4( 1113857

(6)

System (1) is a very complex dynamic system when ai bici di M F E N H and P values are different system (1)performance is complex and dynamic behavior is alsodifferent In this study we set the followinga1 009a2 0025 a3 0012 a4 0165 b1 0422 b2 02b3 08 b4 04 c1 0035 c2 0008 c3 0075c4 0078 d1 0121 d2 0035 d3 00145 d4 0775M 09 F 16 E 295 N 035 H 125 and P 24

By calculation four eigenvalues of the Jacobian matrixJ(O) are λ1 02236 λ2 minus 07845 andλ34 minus 00895 plusmn 00706i Because λi lt 1(i 1 2 3 4) weknow that the equilibrium O(0 0 0 0) is unstable

Let c2 be any value so we can obtain the followingcharacteristic equation

f(λ) λ4 + 074λ3 + 08c2 minus 00683( 1113857λ2

+ 06927c2 minus 00297( 1113857λ minus 00026 + 0036c2 0

(7)

Let p1 074 p2 08c2 minus 00683p3 06927c2 minus 00297 and p4 0036c2 minus 00026According to the Routh-Hurwitz criterion we can obtain thefollowing conditions p1 074gt 0 p1p2 minus p3 gt 0 andp1p2p3 minus p4p

21 minus p2

3 gt 0 By calculation when

4 Complexity

0lt c2 lt 00575 that equilibrium point O(0 0 0 0) isunstable

Now bring the parameter values set above to system (1)By calculation we get the equilibrium pointsS1(minus 14149 0534 37951 minus 05030) S2(135 05868

14901 02367) S3(10838 06617 07819 02)S4(08185 25042 07327 minus 04697) andS5(12523 25109 22876 minus 10085) A similar approachshows the eigenvalue of the equilibrium point S1λ1 minus 07309 λ2 minus 04548 and λ34 02696 plusmn 02758i theeigenvalue of the equilibrium point S2λ1 minus 00314λ2 00665 and λ34 minus 00783 plusmn 01974i the eigenvalue ofthe equilibrium point S3λ1 minus 05057 λ2 minus 00189 andλ34 02068 plusmn 03074i the eigenvalue of the equilibriumpoint S4λ1 00232 λ2 01221 andλ34 minus 01191 plusmn 00801i the eigenvalue of the equilibriumpoint S5 λ1 minus 03009 λ2 01127 andλ34 00519 plusmn 01578i At the equilibrium pointS1(minus 14149 0534 37951 minus 05030) 37951 minus 05030) x(t) isnegative and energy intensity is about 014 Environmentalquality w(t) has reached dynamic equilibrium or graduallyimproved which is an ideal state

nablaV z _x

zx+

z _y

zy+

z _z

zz+

z _w

zw minus 1 +

y

M1113874 1113875a1 +

(F minus 2y)b2

F

minus c3 + minus 1 +y

P1113874 1113875d4

b2 minus a1 minus c3 minus d4 + ya1

Mminus2b2

F+

d4

P1113888 1113889

(8)

When (a1M) minus (2b2F) + (d4P) 0 andb2 minus a1 minus c3 minus d4 lt 0 system (1) is dissipative

22 System Simulation Analysis Numerical simulationanalysis of the system allows us to more intuitively see thecomplex dynamic behavior of the system which plays a veryimportant role in the evolution and stability of the researchsystem Next we will carry out dynamic simulation analysisof the 3E system under the energy reduction constraint andselect the initial value of the system [0015 0758 183 15]

As can be seen from Figure 1 the evolution trajectory ofthe system (1) enters an irregular chaotic state and the shapeof the three-dimensional attractor diagram composed ofdifferent parameters is also different

In addition Figure 2 gives system (1) mixed phase di-agram of a two-dimensional plane in different sections Itcan be seen from Figure 2 that the irregular evolutiontrajectories of system (1) under different cross sections arenot the same which also shows that the chaotic motion isirregular and disordered -e generation of mixed behaviorin the 3E system will have a great impact on the stability ofthe system and also cause problems in the normal operationof the system -e time series diagram of system (1) (x(t)y(t) z(t) and w(t)) is given in Figure 3

Figure 4 shows bifurcation diagram and correspondingLyapunov exponential diagram of the variablec2 isin [0006 0014] change of the four-dimensional system(1) From Figure 4 we find that the four-dimensional system(1) has very complex dynamic behavior As we all know theLyapunov exponential is generally used to determinewhether the system is stable If the maximum Lyapunovexponent of the system is greater than 0 it can be explainedthat the system produces mixed chaotic behavior which is afull manifestation of unstable evolution In this study thedegree of complexity of the four-dimensional 3E systemsunder the constraints of energy reduction is self-evident Ifthe maximum Lyapunov exponent of the system is greater

Table 1 -e specific meanings of each parameter are explained

Parameter Explanation (t isin I I is an economic cycle)a1 -e development coefficient of energy saving and emission reduction x(t)

a2 -e inhibition coefficient of pollution emission y(t) on energy saving and emission reduction x(t)

a3 -e influence coefficient of z(t) input of economic growth on energy saving and emission reduction x(t)

a4 -e influence coefficient of w(t) input of environmental quality on energy saving and emission reduction x(t)

b1 -e influence coefficient of the development of energy saving and emission reduction x(t) on pollution emission y(t)

b2 -e development rate elasticity coefficient of pollution emission y(t)

b3 -e influence coefficient of economic growth z(t) on pollution emission y(t)

b4 -e inhibition coefficient of environmental quality w(t) on pollution emission y(t)

c1 -e influence coefficient of the development of energy saving and emission reduction x(t) on economic growthc2 -e influence coefficient of pollution emission y(t) on economic growth z(t)

c3 -e restraint factor of investment in energy saving and emission reduction x(t) on economic growth z(t)

c4 -e restraint factor of investment in improving environmental quality w(t) on economic growth z(t)

d1-e influence coefficient of the development of energy saving and emission reduction x(t) on the improvement of

environmental quality w(t)

d2 -e inhibition coefficient of pollution emission y(t) on environmental quality w(t)

d3 -e influence coefficient of economic growth z(t)rsquos investment on improving environmental quality w(t)

d4 -e speed coefficient of ecological environment self-repair without external interventionM -e peak value of the impact of pollution emission y(t) on energy saving and emission reduction x(t)

F -e peak value of pollution emission y(t) in an economic cycleE -e peak value of economic growth z(t) in an economic cycleN -e peak value of the impact of energy saving and emission reduction x(t) on economic growth z(t) in an economic cycleH -e peak value of the impact of economic growth z(t) on environmental quality w(t) in an economic cycleP -e maximum amount of pollution that can be contained by the ecological environment

Complexity 5

than or equal to zero we can determine the occurrence ofbifurcation in the four-dimensional system Behavior ismore likely to develop into a chaotic trend

Impact of initial state on the evolution trend of thecomplex four-dimensional dynamical system (1) Figure 5shows the sensitive dependence of complex four-dimensional

2

1z

15

y1 1

x

2

0 0

(a)

02

05w

15

1

z 1x

15

10

(b)

02

05

2

w

15

1

z y

15

110

(c)

02

05w

1

y1 1

x

15

0 0

(d)

Figure 1 -ree-dimensional spatial chaotic attractor phase diagram of system (1)

y

0

05

1

15

2

05 1 150x

(a)

z

05

1

15

2

05 1 150x

(b)

w

0

05

1

15

05 1 150x

(c)

z

05

1

15

2

1 20y

(d)

w

0

05

1

15

1 20y

(e)

w

0

05

1

15

1 15 205z

(f )

Figure 2 Two-dimensional plane chaotic attractor phase diagram of system (1)

6 Complexity

system (1) on initial conditions -e sensitivity of system(when losing stability) with (x y z w) (0015 0758

18315) (x1 y z w) (0014 0758 18315) and(x2 y z w) (0016 0758 18315) and a small change inthe initial conditions may cause a large change in the wholefour-dimensional system which indicates that the system issensitive to the initial state From Figure 5 we can also knowthat the initial values vary greatly in the trajectories of thedeviated system (1) Although the initial states are indistin-guishable the initial values will be quickly established afterseveral iterations which is also an important symbol ofchaotic motion

3 System Parameter Identification

31 Data Gathering On the basis of complex interactions afour-dimensional dynamic system that integrates restrictsand promotes energy conservation energy economy andenvironment is established In this study the determination ofthe parameters of the four-dimensional dynamic system is ofgreat significance to the actual research Because the envi-ronment energy intensity and economic growth are affectedby the changes of these variables based on the official statisticsand measured data of the China Statistical Yearbook geneticoptimization of the optimized LM-BP neural networkmethod

x

y

z

w

0

1

2

02 04 06 08 1 12 14 16 180 2t (103)

ndash10123

02 04 06 08 1 12 14 16 18 20t (103)

115

2

02 04 06 08 1 12 14 16 18 20t (103)

0

1

02 04 06 08 1 12 14 16 18 20t (103)

Figure 3 System (1) time sequences diagram

y

08

1

12

14

16

18

0008 001 0012 00140006c2

(a)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Lyap

unov

expo

nent

s

0008 001 0012 00140006c2

(b)

Figure 4 With c2 isin [0006 0014] change system (1) (a) bifurcation diagram (b) Lyapunov exponential diagram of corresponding (a)

Complexity 7

is used to obtain the actual parameters of the four-dimen-sional system to further analyze the evolutionary relationshipbetween energy consumption energy economic growth andthe environment of the 3E system

In this paper we mainly use the calculation method ofenergy reduction that is now common in the world tocalculate the amount of skill emission reduction [18] -eprincipal component analysis method based on the co-variance matrix is used to calculate the environmentalquality index [1] to represent the data of the environmentalchange Data on energy consumption and economic growthare mainly derived from Chinarsquos official statistical yearbookIn addition in order to make the environmental qualityindex positive during the research process we also use thelogarithmic logic model for data standardization All thedata in Table 2 is a standardized process based on the 1999data -e final data is as follows

32 Model Validation -e LM-BP neural network methodoptimized by genetic algorithm has a good application in theparameter identification of nonlinear systems [1] and it hasgood identification accuracy which makes this methodwidely used in nonidentification of linear system parame-ters After system (1) is discretized the difference equation ofthe following form is obtained

x(k + 1) x(k) + T a1x(k)y

M minus 11113874 1113875 minus a2y + a3z + a4w1113876 1113877

y(k + 1) y(k) + T minus b1x + b2y1 minus y

F1113874 1113875 + b3z

1 minus z

E1113874 1113875 minus b4w1113876 1113877

z(k + 1) z(k) + T c1xx

N minus 11113874 1113875 minus c2y minus c3z minus c4w1113876 1113877

w(k + 1) w(k) + T d1x minus d2y + d3z1 minus z

H1113874 1113875 + d4w

y

P minus 11113874 11138751113876 1113877

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

In this study we used the former n minus 1 group of data asthe input data of the LM-BP neural network optimized bythe genetic algorithm and the post n minus 1 data as the outputdata of the LM-BP neural network optimized by the geneticalgorithm In addition the data needs to be normalized inxi (xi minus xmin)(xmax minus xmin) form All other parameterswill be set to random number and the identified errorcontrol 10minus 6 Finally the identified system parametersare asshown in Table 3

-e data of 1980 is selected as the initial value of system[000000085 0658 173 11211] and the true validity of theidentification parameters is further verified -e evolutiontrajectory of the system is shown in Figures 6 and 7 It can beseen from the phase diagram of the evolutionary trajectoryof the system that the evolution trajectory of the system ismulticycle and can always be in a stable mode -is explainsthe true effectiveness of the system from the side which isalso in line with the real situation

4 System Parameter Analysis

In order to fully understand the stability of the above four-dimensional system (1) as well as the changes and impacts ofenergy intensity how to effectively reduce energy intensitystabilize economic development improve the quality ofecological environment and seek for high-quality sus-tainable development models and strategies and suggestionsfor the coordinated development of energy economy andenvironment therefore it is necessary to conduct an in-depth analysis of some key parameters of the four-dimen-sional system (1)

In Figures 8(a) and 8(b) we can find that althoughincreasing the investment in energy saving and emissionreduction can effectively improve the environmental qualitythe effect on reducing energy intensity is not obvious Overtime the amplitudes of the evolutionary fluctuations ofenergy intensity and environmental quality oscillate around

0

02

04

06

08

1

12

14

16

Erro

r sta

rtin

g fro

m d

iffer

ent i

nitia

l con

ditio

ns

05 2 3 45351 415 25 50t (103)

x (x = 0016)x (x = 0015)x (x = 0014)

Figure 5 System (1) sensitivity analysis

Table 2 Statistics on energy reduction energy consumption GDPand environment in China

Year x y z w

2000 19626 10455 11085 098372001 36786 11066 12228 095952002 22791 12064 13482 093472003 12699 14020 15283 087472004 23033 16382 18062 077412005 19352 18594 20813 072422006 20778 20380 24509 064032007 39437 22156 30307 054552008 65583 22808 35976 047522009 32830 23912 38997 040612010 33307 25656 46020 036932011 36871 27534 54243 035652012 40130 28608 60326 032102013 39274 29659 66068 028172014 42167 30292 72151 025752015 42893 30583 76813 023222016 45925 31004 82872 021592017 46121 31942 92297 02147

8 Complexity

Tabl

e3

System

(1)identifi

estheactual

parameters

a1

a2

a3

a4

b1

b2

b3

b4

c 1c 2

c 3c 4

d1

d2

d3

d4

MF

EN

HP

01277

02338

01992

00115

01896

04325

03818

00141

07582

05265

05834

00534

00591

00191

02567

05892

06523

05816

06437

05573

06943

07121

Complexity 9

a certain value In a relatively short period of time theimprovement of environmental quality is also very obviousbut in the long run the environment is still deteriorating

with the decline in the discount rate of energy-saving andemission-reduction inputs -e oscillating amplitude ofenergy intensity will decrease significantly with the increase

2

1

008

0604

02ndash04

0y x

z

(a)

ndash040

x

w

z

1

05

0

ndash052

10

(b)

1

05

0

ndash05

w

z y

21

0 0204

0608

(c)

1

05

0

ndash05

w

0806

0402y ndash04

0x

(d)

Figure 6 -ree-dimensional spatial phase diagram of system (1) with identified parameters

08

06

04

02

y

xndash04ndash06 ndash02 0

(a)

2

1

0

z

xndash04 ndash02ndash06 0

(b)

w

xndash04 ndash02ndash06 0

1

0

ndash1

(c)

2

1

0

02 04 06 08

z

y

(d)

02 04 06 08y

w

1

0

ndash1

(e)

z

w

1

0

ndash10 1 2

(f )

Figure 7 Two-dimensional plane phase diagram of system (1) with identified parameters

10 Complexity

of energy-saving and emission-reduction input but there isno obvious effect on the peak energy intensity -erefore itis not obvious that the effect of reducing the energy intensityand improving the stability of environmental quality bysimply increasing the investment in energy saving andemission reduction is not obvious

From Figures 9(a) and 9(b) we can find that when thepeak value of pollution emissions F 05816 the evolutiontrajectories of energy intensity and environmental qualityshow fluctuations around a certain central value over time-is phenomenon will be very unfavorable to the im-provement of environmental quality in controlling pollutionemissions (ie the inability to effectively reflect the energyreduction policies) when F 04816 with the passage oftime energy intensity and environmental quality are stillfluctuating up and down at a certain central value but willgradually shrink with the magnitude of evolutionary fluc-tuations and the maximum peak of energy intensity is alsosignificantly smaller than before It also has a significantimpact on the evolution of environmental quality In thelong run the central value of the shock is decreasing theamplitude of the shock is decreasing and eventually it tendsto be stable After the pollution emission peak is loweredagain F 03816 the energy intensity and environmentalquality evolve to a stable value at a relatively fast rate and thepeak value of the energy intensity and the center value of theoscillation are reduced again before comparison -ereforeit can be better explained that effective control of the peakarrival time of pollution emissions can be used as an im-portant decision for pollution emission control and energyintensity reduction

From Figure 9(b) we can also find that the advance ofthe peak of pollution emissions makes the environmentalsystem take the risk ahead and the threat level is greatlyincreased -e reason for this phenomenon is that the peakof pollution discharge exceeds the self-purification speed ofthe natural environment system during the self-circulationprocess so that the accumulation of pollutants in the eco-logical environment system reaches the maximum capacityand the self-purification ability of the environmental system

is weakened In a relatively short period of time the eco-logical environment system is extremely deteriorated-erefore how to effectively and reasonably control the peakof pollution emission is very important for controlling thestability of 3E system and improving the environmentalquality

By comparing Figure 10(a) it can be found that in theshort term the environmental capacity of the ecosystem hasno significant effect on the stability of the evolution of the 3Esystem As the environmental capacity decreases over timethe evolution of environmental quality shows an upwardtrend of fluctuations and fluctuations around a certaincentral value when the capacity of the ecosystem falls to thelimit (ie the pollution effect exceeds the ecological envi-ronment) the system collapses (ie the ecological envi-ronment disappears and the ecosystem can no longer relyon self-regulation to repair the ecological environment) As aresult this situation continues and the ecological environ-ment is eventually sold out It is confirmed that the eco-logical environment system has a certain bearing capacityand the effect that the ecosystem will not be in operation orself-purification after the limit value can be exceeded is notsignificant

From Figure 10(b) we can find that the effect of simplyincreasing the economic investment in the environment toimprove the environmental quality is not obvious it doesnot increase the economic investment as expected and theenvironment can be effectively improved From the evolu-tionary trajectory of the system it can be seen that theevolutionary trajectory of the system revolves around centralvalue fluctuation and oscillation amplitude over time -isphenomenon shows that the effects of economic input in theprocess of environmental governance are not significantenough -erefore in order to improve the quality of theecological environment and promote the rapid developmentof the economy we need more measures to use more meansand technologies to promote stable economic growth andmanagement of the ecological environment It is necessaryto correctly grasp the ecological environment protection andthe relationship between economic developments explore

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash4

ndash3

ndash2

ndash1

0

1

2

Envi

ronm

enta

l qua

lity

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

(b)

Figure 8 -e parameters a3 on the influence of system (1)

Complexity 11

synergies to promote ecological priorities and green de-velopment new ideas and ultimately achieve a ldquowin-winrdquoenvironment and economy

5 Conclusion

In this study the energy economic and environmental (3E)four-dimensional system model of energy conservationconstraints was first established -e Bayesian estimationmethod is used to correct the environmental quality vari-ables to obtain the environmental quality data needed for theresearch In addition based on the Chinese statisticalyearbook data the LevenbergndashMarquardt BP neural net-work method optimized by genetic algorithm is used toenergy economy and environment under energy conser-vation constraints -e parameters in the four-dimensionalsystem model are effectively identified Finally the systemscience analysis theory and complex system dynamics theoryare used to analyze the stability and complex dynamics of the

model and explore the influence of some key parameters inthe four-dimensional system on the evolution stability of thesystem -e main conclusions are as follows

(1) Although increasing the investment in energy re-duction can effectively improve the environmentalquality in a relatively short period of time theimprovement of environmental quality is also veryobvious but in the long run the environment is stilldeteriorating with the decline in the discount rate ofenergy reduction inputs

(2) It can be better explained that effective control of thepeak arrival time of pollution emissions can be usedas an important decision for pollution emissioncontrol and energy intensity reduction thereforehow to effectively and reasonably control the peak ofpollution emissions is of great significance forcontrolling the stability of energy economy andenvironment system under the constraint of energy

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

(b)

Figure 9 -e parameters F on the influence of system (1)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redP = 05121 blue P = 06121 and green

P = 07121)

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redd3 = 02667 blue d3 = 03667 and green

d3 = 04667)

(b)

Figure 10 -e different parameters P and d3 on the influence of system (1)

12 Complexity

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

is an interwoven and interactive relationship which can beexpressed by the connection weights and thresholds betweennodes in each layer Compared with the traditional multipleregression prediction method this expression has better fittingability and precision BP neural network has strong nonlinearfunction approximation ability and has been widely used in timeseries analysis and financial forecasting BP neural network hasthe ability to fit the function and determine the weights andthresholds between neurons through learning process [39]-erefore we depended on the official statistics and measureddata of the China Statistical Yearbook to predict the future trendof 3E

In the process of enhancing environment governance wehave seenmore complicated environmental issues for which it ismore difficult to find solutions With that we see even moredifficulties and complexity for the various projects to furtherstrengthen environment governance and environmental qualityimprovement Presently industrialization urbanization andmodernization have propelled energy demand at a growth stageOngoing consumption increase in fossil fuels with high pollutionand high carbon emission has impeded the sustainable devel-opment for the environment -erefore we need to fully realizethe dynamic complexity of the 3E system and the lag of en-vironmental protection in order to reduce the damage moreeffectively and rationally to the ecological environment systemand make the economy sustainable

With the rapid development of environmental protec-tion the gradual improvement of social-environmentalawareness and the increasing competition in the industrythe environmental governance network is a complexadaptive system formed by the game and interest coordi-nation and self-organization under the market operationmechanism -erefore the research on 3E systems needs topay more attention to the complexity brought by multi-system interaction In general 3E is increasingly showing thedynamic complexity of the system -erefore it is necessaryto study how the three systems of the main body establish aneffective coordination strategy mechanism and study theenvironmental governance network and economy based onsuch microbehavior and game characteristics Develop amacrointegrated structure and a mechanism for the for-mation of good performance in particular the emergence ofthe overall structure and performance of 3E systems and thesystematic analysis between environmental and economicsystems In the meantime judging from the current researchthat concerns the impact of environmental governance andenvironmental governance system engineering and divingdeeply into current study we believe that the followingaspects need to be enhanced and perfected Study the fol-lowing issues First based on the research foundation of therelationship of the dual systems we need to integrate the 3Einto the system analysis by developing theoretical analysesbased on the multiple systemsrsquo coordination and develop-ment angles Secondly we need to study the evaluationpattern of the 3Ersquos complexity -irdly the official data areused to identify the 3E system parameters and the evolutionof the 3E system analyzed It is under such current situationthat the 3E systemrsquos variation pattern would be of signifi-cance to the systemrsquos sustainable development

-is study makes a series of significant contributions tothe research of the 3Ersquos complexity

First this study considers the inclusion of energy re-duction constraints on the 3E system proposed and gets anew four-dimensional system which is more in line withthe actual situation and the current development needsSecond this study deviates from the leading research onenergy-economy-environment systems research that fo-cuses primarily on environmental impact analysis [40]global environmental development [41] eco-industrialsystems planning [42 43] dynamic assessment of urbaneconomy-resource-environment systems [44] and eco-nomic and environmentally sustainable development[45] Here through the stability analysis of dynamic 3Esystem by system complexity theory the gap in meth-odology commonly used in 3E system research is bridged-e results provide a practical policy prescription foreffective pollution control-ird based on the official data the Levenberg-Mar-quardt backpropagation neural network method wasoptimized by genetic algorithm to effectively identifythe parameters in the 3E system which is more con-ducive to better research on the interaction betweenvarious elements of the 3E system

-is paper is organized as follows In Section 2 we con-struct a 3E system with energy-constrained constraints andtheoretically analyze the system through the theory of com-plexity and use numerical simulation to demonstrate thevarious dynamic behaviors of the four-dimensional system InSection 3 the genetic algorithm is used to optimize the LM-BPneural network method to identify and confirm the systemparameters of the four-dimensional system In Section 4 an in-depth analysis of the changes in key parameters of the system iscarried out to study the stability and dynamic complexity of thesystem Finally the main conclusions of this study are given

2 Model Construct and Theoretical Analysis

21ModelConstruct In the paper we consider the inclusionof energy reduction constraints on the 3E system proposedby Zhao et al [1] and get a new four-dimensional systemwhich is more in line with the actual situation and thecurrent development needs Energy economy and envi-ronment (3E) system containing energy reduction con-straints is given in the following form

_x a1xy

M minus 11113874 1113875 minus a2y + a3z + a4w

_y minus b1x + b2y1 minus y

F1113874 1113875 + b3z

1 minus z

E1113874 1113875 minus b4w

_z c1xx

N minus 11113874 1113875 minus c2y minus c3z minus c4w

_w d1x minus d2y + d3z1 minus z

H1113874 1113875 + d4w

y

P minus 11113874 1113875

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

Complexity 3

where x(t) y(t) z(t) are w(t) respectively the level ofenergy conservation and emission reduction pollutionemission economic growth (GDP) and environmentalquality in period t ai bi ci di (i 1 2 3 4) M F E N Hand P are normal numbers t isin I and I is an economic cycle(Table 1)

In system (1) _x represents the change level of energysaving and emission reduction in t period _y represents thelevel of change in pollution emissions in t period _z rep-resents the growth level of economic growth in the t period_w represents the change level of environmental quality in t

period When the impact of pollution exceeds the maximumcapacity of the ecological environment (that _wgt 0) it meansthat the ecological environment is deteriorating In this casethe ecosystem cannot rely on self-regulation to repair-erefore when this situation continues the ecologicalenvironment will eventually be sold out when _wle 0 itmeans that the environmental quality has reached a dynamicbalance or gradually improved and only under this con-dition can the ecological environment be the basis of humansocial development [46ndash48]

By system (1) energy intensity can be launched the formof energy intensity is as follows

energy intensity A economic cycle energy consumption

GDPwithin an economic cycle

(2)

Next we will analyze the dynamics of 3E system con-taining energy reduction constraints By calculation theJacobian matrix of the system (1) can be obtained as follows

J

y

Mminus 11113874 1113875a1

xa1

Mminus a2 a3 a4

minus b1(F minus 2y)b2

F

(E minus 2z)b3

Eminus b4

minus(N minus 2x)c1

Nminus c2 minus c3 minus c4

d1 minus d2 +wd4

P

(H minus 2z)d3

H

y

P minus 1minus 11113874 1113875d4

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)

-e six real equilibrium points of the 3E system (1) arerespectively O(0 0 0 0) S1(x1 y1 z1 w1)S2(x2 y2 z2 w2) S3(x3 y3 z3 w3) S4(x4 y4 z4 w4) andS5(x5 y5 z5 w5) -e Jacobian matrix of system (1) atequilibrium point O(0 0 0 0) is of the following form

J0

minus a1 minus a2 a3 a4

minus b1 b2 b3 minus b4

minus c1 minus c2 minus c3 minus c4

d1 minus d2 d3 minus d4

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

So the characteristic polynomial of J(O) is as follows

f(λ) λ4 + Aλ3 + Bλ2 + Cλ + D 0 (5)

where

A a1 minus b2 + c3 + d4

B a3c1 minus a2b1 + b3c2 minus b2c3 minus a4d1 + b4d2 + c4d3 minus b2d4 + c3d4 + a1 c3 + d4 minus b2( 1113857

C a1b3c2 minus a1b2c3 + a4b2d1 minus a4c3d1 minus a4b1d2 + a1b4d2 + b4c3d2 minus b3c4d2

+ a4c1d3 + b4c2d3 + a1c4d3 minus b2c4d3 minus a1b2d4 + b3c2d4 + a1c3d4 minus b2c3d4

+ a3 c4d1 + c1d4 minus b2c1 minus b1c2( 1113857 minus a2 b3c1 minus b4d1 + b1 c3 + d4( 1113857( 1113857

D a2b4c3d1 minus a2b3c4d1 + a1b4c3d2 minus a1b3c4d2 minus a2b4c1d3 + a1b4c2d3 minus a2b1c4d3 minus a1b2c4d3

minus a4 b3c2d1 minus b2c3d1 + b3c1d2 + b1c3d2 + b2c1d3 + b1c2d3( 1113857 minus a2b3c1d4 + a1b3c2d4

minus a2b1c3d4 minus a1b2c3d4 + a3 b4c2d1 minus b2c4d1 + b4c1d2 + b1c4d2 minus b2c1d4 minus b1c2d4( 1113857

(6)

System (1) is a very complex dynamic system when ai bici di M F E N H and P values are different system (1)performance is complex and dynamic behavior is alsodifferent In this study we set the followinga1 009a2 0025 a3 0012 a4 0165 b1 0422 b2 02b3 08 b4 04 c1 0035 c2 0008 c3 0075c4 0078 d1 0121 d2 0035 d3 00145 d4 0775M 09 F 16 E 295 N 035 H 125 and P 24

By calculation four eigenvalues of the Jacobian matrixJ(O) are λ1 02236 λ2 minus 07845 andλ34 minus 00895 plusmn 00706i Because λi lt 1(i 1 2 3 4) weknow that the equilibrium O(0 0 0 0) is unstable

Let c2 be any value so we can obtain the followingcharacteristic equation

f(λ) λ4 + 074λ3 + 08c2 minus 00683( 1113857λ2

+ 06927c2 minus 00297( 1113857λ minus 00026 + 0036c2 0

(7)

Let p1 074 p2 08c2 minus 00683p3 06927c2 minus 00297 and p4 0036c2 minus 00026According to the Routh-Hurwitz criterion we can obtain thefollowing conditions p1 074gt 0 p1p2 minus p3 gt 0 andp1p2p3 minus p4p

21 minus p2

3 gt 0 By calculation when

4 Complexity

0lt c2 lt 00575 that equilibrium point O(0 0 0 0) isunstable

Now bring the parameter values set above to system (1)By calculation we get the equilibrium pointsS1(minus 14149 0534 37951 minus 05030) S2(135 05868

14901 02367) S3(10838 06617 07819 02)S4(08185 25042 07327 minus 04697) andS5(12523 25109 22876 minus 10085) A similar approachshows the eigenvalue of the equilibrium point S1λ1 minus 07309 λ2 minus 04548 and λ34 02696 plusmn 02758i theeigenvalue of the equilibrium point S2λ1 minus 00314λ2 00665 and λ34 minus 00783 plusmn 01974i the eigenvalue ofthe equilibrium point S3λ1 minus 05057 λ2 minus 00189 andλ34 02068 plusmn 03074i the eigenvalue of the equilibriumpoint S4λ1 00232 λ2 01221 andλ34 minus 01191 plusmn 00801i the eigenvalue of the equilibriumpoint S5 λ1 minus 03009 λ2 01127 andλ34 00519 plusmn 01578i At the equilibrium pointS1(minus 14149 0534 37951 minus 05030) 37951 minus 05030) x(t) isnegative and energy intensity is about 014 Environmentalquality w(t) has reached dynamic equilibrium or graduallyimproved which is an ideal state

nablaV z _x

zx+

z _y

zy+

z _z

zz+

z _w

zw minus 1 +

y

M1113874 1113875a1 +

(F minus 2y)b2

F

minus c3 + minus 1 +y

P1113874 1113875d4

b2 minus a1 minus c3 minus d4 + ya1

Mminus2b2

F+

d4

P1113888 1113889

(8)

When (a1M) minus (2b2F) + (d4P) 0 andb2 minus a1 minus c3 minus d4 lt 0 system (1) is dissipative

22 System Simulation Analysis Numerical simulationanalysis of the system allows us to more intuitively see thecomplex dynamic behavior of the system which plays a veryimportant role in the evolution and stability of the researchsystem Next we will carry out dynamic simulation analysisof the 3E system under the energy reduction constraint andselect the initial value of the system [0015 0758 183 15]

As can be seen from Figure 1 the evolution trajectory ofthe system (1) enters an irregular chaotic state and the shapeof the three-dimensional attractor diagram composed ofdifferent parameters is also different

In addition Figure 2 gives system (1) mixed phase di-agram of a two-dimensional plane in different sections Itcan be seen from Figure 2 that the irregular evolutiontrajectories of system (1) under different cross sections arenot the same which also shows that the chaotic motion isirregular and disordered -e generation of mixed behaviorin the 3E system will have a great impact on the stability ofthe system and also cause problems in the normal operationof the system -e time series diagram of system (1) (x(t)y(t) z(t) and w(t)) is given in Figure 3

Figure 4 shows bifurcation diagram and correspondingLyapunov exponential diagram of the variablec2 isin [0006 0014] change of the four-dimensional system(1) From Figure 4 we find that the four-dimensional system(1) has very complex dynamic behavior As we all know theLyapunov exponential is generally used to determinewhether the system is stable If the maximum Lyapunovexponent of the system is greater than 0 it can be explainedthat the system produces mixed chaotic behavior which is afull manifestation of unstable evolution In this study thedegree of complexity of the four-dimensional 3E systemsunder the constraints of energy reduction is self-evident Ifthe maximum Lyapunov exponent of the system is greater

Table 1 -e specific meanings of each parameter are explained

Parameter Explanation (t isin I I is an economic cycle)a1 -e development coefficient of energy saving and emission reduction x(t)

a2 -e inhibition coefficient of pollution emission y(t) on energy saving and emission reduction x(t)

a3 -e influence coefficient of z(t) input of economic growth on energy saving and emission reduction x(t)

a4 -e influence coefficient of w(t) input of environmental quality on energy saving and emission reduction x(t)

b1 -e influence coefficient of the development of energy saving and emission reduction x(t) on pollution emission y(t)

b2 -e development rate elasticity coefficient of pollution emission y(t)

b3 -e influence coefficient of economic growth z(t) on pollution emission y(t)

b4 -e inhibition coefficient of environmental quality w(t) on pollution emission y(t)

c1 -e influence coefficient of the development of energy saving and emission reduction x(t) on economic growthc2 -e influence coefficient of pollution emission y(t) on economic growth z(t)

c3 -e restraint factor of investment in energy saving and emission reduction x(t) on economic growth z(t)

c4 -e restraint factor of investment in improving environmental quality w(t) on economic growth z(t)

d1-e influence coefficient of the development of energy saving and emission reduction x(t) on the improvement of

environmental quality w(t)

d2 -e inhibition coefficient of pollution emission y(t) on environmental quality w(t)

d3 -e influence coefficient of economic growth z(t)rsquos investment on improving environmental quality w(t)

d4 -e speed coefficient of ecological environment self-repair without external interventionM -e peak value of the impact of pollution emission y(t) on energy saving and emission reduction x(t)

F -e peak value of pollution emission y(t) in an economic cycleE -e peak value of economic growth z(t) in an economic cycleN -e peak value of the impact of energy saving and emission reduction x(t) on economic growth z(t) in an economic cycleH -e peak value of the impact of economic growth z(t) on environmental quality w(t) in an economic cycleP -e maximum amount of pollution that can be contained by the ecological environment

Complexity 5

than or equal to zero we can determine the occurrence ofbifurcation in the four-dimensional system Behavior ismore likely to develop into a chaotic trend

Impact of initial state on the evolution trend of thecomplex four-dimensional dynamical system (1) Figure 5shows the sensitive dependence of complex four-dimensional

2

1z

15

y1 1

x

2

0 0

(a)

02

05w

15

1

z 1x

15

10

(b)

02

05

2

w

15

1

z y

15

110

(c)

02

05w

1

y1 1

x

15

0 0

(d)

Figure 1 -ree-dimensional spatial chaotic attractor phase diagram of system (1)

y

0

05

1

15

2

05 1 150x

(a)

z

05

1

15

2

05 1 150x

(b)

w

0

05

1

15

05 1 150x

(c)

z

05

1

15

2

1 20y

(d)

w

0

05

1

15

1 20y

(e)

w

0

05

1

15

1 15 205z

(f )

Figure 2 Two-dimensional plane chaotic attractor phase diagram of system (1)

6 Complexity

system (1) on initial conditions -e sensitivity of system(when losing stability) with (x y z w) (0015 0758

18315) (x1 y z w) (0014 0758 18315) and(x2 y z w) (0016 0758 18315) and a small change inthe initial conditions may cause a large change in the wholefour-dimensional system which indicates that the system issensitive to the initial state From Figure 5 we can also knowthat the initial values vary greatly in the trajectories of thedeviated system (1) Although the initial states are indistin-guishable the initial values will be quickly established afterseveral iterations which is also an important symbol ofchaotic motion

3 System Parameter Identification

31 Data Gathering On the basis of complex interactions afour-dimensional dynamic system that integrates restrictsand promotes energy conservation energy economy andenvironment is established In this study the determination ofthe parameters of the four-dimensional dynamic system is ofgreat significance to the actual research Because the envi-ronment energy intensity and economic growth are affectedby the changes of these variables based on the official statisticsand measured data of the China Statistical Yearbook geneticoptimization of the optimized LM-BP neural networkmethod

x

y

z

w

0

1

2

02 04 06 08 1 12 14 16 180 2t (103)

ndash10123

02 04 06 08 1 12 14 16 18 20t (103)

115

2

02 04 06 08 1 12 14 16 18 20t (103)

0

1

02 04 06 08 1 12 14 16 18 20t (103)

Figure 3 System (1) time sequences diagram

y

08

1

12

14

16

18

0008 001 0012 00140006c2

(a)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Lyap

unov

expo

nent

s

0008 001 0012 00140006c2

(b)

Figure 4 With c2 isin [0006 0014] change system (1) (a) bifurcation diagram (b) Lyapunov exponential diagram of corresponding (a)

Complexity 7

is used to obtain the actual parameters of the four-dimen-sional system to further analyze the evolutionary relationshipbetween energy consumption energy economic growth andthe environment of the 3E system

In this paper we mainly use the calculation method ofenergy reduction that is now common in the world tocalculate the amount of skill emission reduction [18] -eprincipal component analysis method based on the co-variance matrix is used to calculate the environmentalquality index [1] to represent the data of the environmentalchange Data on energy consumption and economic growthare mainly derived from Chinarsquos official statistical yearbookIn addition in order to make the environmental qualityindex positive during the research process we also use thelogarithmic logic model for data standardization All thedata in Table 2 is a standardized process based on the 1999data -e final data is as follows

32 Model Validation -e LM-BP neural network methodoptimized by genetic algorithm has a good application in theparameter identification of nonlinear systems [1] and it hasgood identification accuracy which makes this methodwidely used in nonidentification of linear system parame-ters After system (1) is discretized the difference equation ofthe following form is obtained

x(k + 1) x(k) + T a1x(k)y

M minus 11113874 1113875 minus a2y + a3z + a4w1113876 1113877

y(k + 1) y(k) + T minus b1x + b2y1 minus y

F1113874 1113875 + b3z

1 minus z

E1113874 1113875 minus b4w1113876 1113877

z(k + 1) z(k) + T c1xx

N minus 11113874 1113875 minus c2y minus c3z minus c4w1113876 1113877

w(k + 1) w(k) + T d1x minus d2y + d3z1 minus z

H1113874 1113875 + d4w

y

P minus 11113874 11138751113876 1113877

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

In this study we used the former n minus 1 group of data asthe input data of the LM-BP neural network optimized bythe genetic algorithm and the post n minus 1 data as the outputdata of the LM-BP neural network optimized by the geneticalgorithm In addition the data needs to be normalized inxi (xi minus xmin)(xmax minus xmin) form All other parameterswill be set to random number and the identified errorcontrol 10minus 6 Finally the identified system parametersare asshown in Table 3

-e data of 1980 is selected as the initial value of system[000000085 0658 173 11211] and the true validity of theidentification parameters is further verified -e evolutiontrajectory of the system is shown in Figures 6 and 7 It can beseen from the phase diagram of the evolutionary trajectoryof the system that the evolution trajectory of the system ismulticycle and can always be in a stable mode -is explainsthe true effectiveness of the system from the side which isalso in line with the real situation

4 System Parameter Analysis

In order to fully understand the stability of the above four-dimensional system (1) as well as the changes and impacts ofenergy intensity how to effectively reduce energy intensitystabilize economic development improve the quality ofecological environment and seek for high-quality sus-tainable development models and strategies and suggestionsfor the coordinated development of energy economy andenvironment therefore it is necessary to conduct an in-depth analysis of some key parameters of the four-dimen-sional system (1)

In Figures 8(a) and 8(b) we can find that althoughincreasing the investment in energy saving and emissionreduction can effectively improve the environmental qualitythe effect on reducing energy intensity is not obvious Overtime the amplitudes of the evolutionary fluctuations ofenergy intensity and environmental quality oscillate around

0

02

04

06

08

1

12

14

16

Erro

r sta

rtin

g fro

m d

iffer

ent i

nitia

l con

ditio

ns

05 2 3 45351 415 25 50t (103)

x (x = 0016)x (x = 0015)x (x = 0014)

Figure 5 System (1) sensitivity analysis

Table 2 Statistics on energy reduction energy consumption GDPand environment in China

Year x y z w

2000 19626 10455 11085 098372001 36786 11066 12228 095952002 22791 12064 13482 093472003 12699 14020 15283 087472004 23033 16382 18062 077412005 19352 18594 20813 072422006 20778 20380 24509 064032007 39437 22156 30307 054552008 65583 22808 35976 047522009 32830 23912 38997 040612010 33307 25656 46020 036932011 36871 27534 54243 035652012 40130 28608 60326 032102013 39274 29659 66068 028172014 42167 30292 72151 025752015 42893 30583 76813 023222016 45925 31004 82872 021592017 46121 31942 92297 02147

8 Complexity

Tabl

e3

System

(1)identifi

estheactual

parameters

a1

a2

a3

a4

b1

b2

b3

b4

c 1c 2

c 3c 4

d1

d2

d3

d4

MF

EN

HP

01277

02338

01992

00115

01896

04325

03818

00141

07582

05265

05834

00534

00591

00191

02567

05892

06523

05816

06437

05573

06943

07121

Complexity 9

a certain value In a relatively short period of time theimprovement of environmental quality is also very obviousbut in the long run the environment is still deteriorating

with the decline in the discount rate of energy-saving andemission-reduction inputs -e oscillating amplitude ofenergy intensity will decrease significantly with the increase

2

1

008

0604

02ndash04

0y x

z

(a)

ndash040

x

w

z

1

05

0

ndash052

10

(b)

1

05

0

ndash05

w

z y

21

0 0204

0608

(c)

1

05

0

ndash05

w

0806

0402y ndash04

0x

(d)

Figure 6 -ree-dimensional spatial phase diagram of system (1) with identified parameters

08

06

04

02

y

xndash04ndash06 ndash02 0

(a)

2

1

0

z

xndash04 ndash02ndash06 0

(b)

w

xndash04 ndash02ndash06 0

1

0

ndash1

(c)

2

1

0

02 04 06 08

z

y

(d)

02 04 06 08y

w

1

0

ndash1

(e)

z

w

1

0

ndash10 1 2

(f )

Figure 7 Two-dimensional plane phase diagram of system (1) with identified parameters

10 Complexity

of energy-saving and emission-reduction input but there isno obvious effect on the peak energy intensity -erefore itis not obvious that the effect of reducing the energy intensityand improving the stability of environmental quality bysimply increasing the investment in energy saving andemission reduction is not obvious

From Figures 9(a) and 9(b) we can find that when thepeak value of pollution emissions F 05816 the evolutiontrajectories of energy intensity and environmental qualityshow fluctuations around a certain central value over time-is phenomenon will be very unfavorable to the im-provement of environmental quality in controlling pollutionemissions (ie the inability to effectively reflect the energyreduction policies) when F 04816 with the passage oftime energy intensity and environmental quality are stillfluctuating up and down at a certain central value but willgradually shrink with the magnitude of evolutionary fluc-tuations and the maximum peak of energy intensity is alsosignificantly smaller than before It also has a significantimpact on the evolution of environmental quality In thelong run the central value of the shock is decreasing theamplitude of the shock is decreasing and eventually it tendsto be stable After the pollution emission peak is loweredagain F 03816 the energy intensity and environmentalquality evolve to a stable value at a relatively fast rate and thepeak value of the energy intensity and the center value of theoscillation are reduced again before comparison -ereforeit can be better explained that effective control of the peakarrival time of pollution emissions can be used as an im-portant decision for pollution emission control and energyintensity reduction

From Figure 9(b) we can also find that the advance ofthe peak of pollution emissions makes the environmentalsystem take the risk ahead and the threat level is greatlyincreased -e reason for this phenomenon is that the peakof pollution discharge exceeds the self-purification speed ofthe natural environment system during the self-circulationprocess so that the accumulation of pollutants in the eco-logical environment system reaches the maximum capacityand the self-purification ability of the environmental system

is weakened In a relatively short period of time the eco-logical environment system is extremely deteriorated-erefore how to effectively and reasonably control the peakof pollution emission is very important for controlling thestability of 3E system and improving the environmentalquality

By comparing Figure 10(a) it can be found that in theshort term the environmental capacity of the ecosystem hasno significant effect on the stability of the evolution of the 3Esystem As the environmental capacity decreases over timethe evolution of environmental quality shows an upwardtrend of fluctuations and fluctuations around a certaincentral value when the capacity of the ecosystem falls to thelimit (ie the pollution effect exceeds the ecological envi-ronment) the system collapses (ie the ecological envi-ronment disappears and the ecosystem can no longer relyon self-regulation to repair the ecological environment) As aresult this situation continues and the ecological environ-ment is eventually sold out It is confirmed that the eco-logical environment system has a certain bearing capacityand the effect that the ecosystem will not be in operation orself-purification after the limit value can be exceeded is notsignificant

From Figure 10(b) we can find that the effect of simplyincreasing the economic investment in the environment toimprove the environmental quality is not obvious it doesnot increase the economic investment as expected and theenvironment can be effectively improved From the evolu-tionary trajectory of the system it can be seen that theevolutionary trajectory of the system revolves around centralvalue fluctuation and oscillation amplitude over time -isphenomenon shows that the effects of economic input in theprocess of environmental governance are not significantenough -erefore in order to improve the quality of theecological environment and promote the rapid developmentof the economy we need more measures to use more meansand technologies to promote stable economic growth andmanagement of the ecological environment It is necessaryto correctly grasp the ecological environment protection andthe relationship between economic developments explore

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash4

ndash3

ndash2

ndash1

0

1

2

Envi

ronm

enta

l qua

lity

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

(b)

Figure 8 -e parameters a3 on the influence of system (1)

Complexity 11

synergies to promote ecological priorities and green de-velopment new ideas and ultimately achieve a ldquowin-winrdquoenvironment and economy

5 Conclusion

In this study the energy economic and environmental (3E)four-dimensional system model of energy conservationconstraints was first established -e Bayesian estimationmethod is used to correct the environmental quality vari-ables to obtain the environmental quality data needed for theresearch In addition based on the Chinese statisticalyearbook data the LevenbergndashMarquardt BP neural net-work method optimized by genetic algorithm is used toenergy economy and environment under energy conser-vation constraints -e parameters in the four-dimensionalsystem model are effectively identified Finally the systemscience analysis theory and complex system dynamics theoryare used to analyze the stability and complex dynamics of the

model and explore the influence of some key parameters inthe four-dimensional system on the evolution stability of thesystem -e main conclusions are as follows

(1) Although increasing the investment in energy re-duction can effectively improve the environmentalquality in a relatively short period of time theimprovement of environmental quality is also veryobvious but in the long run the environment is stilldeteriorating with the decline in the discount rate ofenergy reduction inputs

(2) It can be better explained that effective control of thepeak arrival time of pollution emissions can be usedas an important decision for pollution emissioncontrol and energy intensity reduction thereforehow to effectively and reasonably control the peak ofpollution emissions is of great significance forcontrolling the stability of energy economy andenvironment system under the constraint of energy

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

(b)

Figure 9 -e parameters F on the influence of system (1)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redP = 05121 blue P = 06121 and green

P = 07121)

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redd3 = 02667 blue d3 = 03667 and green

d3 = 04667)

(b)

Figure 10 -e different parameters P and d3 on the influence of system (1)

12 Complexity

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

where x(t) y(t) z(t) are w(t) respectively the level ofenergy conservation and emission reduction pollutionemission economic growth (GDP) and environmentalquality in period t ai bi ci di (i 1 2 3 4) M F E N Hand P are normal numbers t isin I and I is an economic cycle(Table 1)

In system (1) _x represents the change level of energysaving and emission reduction in t period _y represents thelevel of change in pollution emissions in t period _z rep-resents the growth level of economic growth in the t period_w represents the change level of environmental quality in t

period When the impact of pollution exceeds the maximumcapacity of the ecological environment (that _wgt 0) it meansthat the ecological environment is deteriorating In this casethe ecosystem cannot rely on self-regulation to repair-erefore when this situation continues the ecologicalenvironment will eventually be sold out when _wle 0 itmeans that the environmental quality has reached a dynamicbalance or gradually improved and only under this con-dition can the ecological environment be the basis of humansocial development [46ndash48]

By system (1) energy intensity can be launched the formof energy intensity is as follows

energy intensity A economic cycle energy consumption

GDPwithin an economic cycle

(2)

Next we will analyze the dynamics of 3E system con-taining energy reduction constraints By calculation theJacobian matrix of the system (1) can be obtained as follows

J

y

Mminus 11113874 1113875a1

xa1

Mminus a2 a3 a4

minus b1(F minus 2y)b2

F

(E minus 2z)b3

Eminus b4

minus(N minus 2x)c1

Nminus c2 minus c3 minus c4

d1 minus d2 +wd4

P

(H minus 2z)d3

H

y

P minus 1minus 11113874 1113875d4

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)

-e six real equilibrium points of the 3E system (1) arerespectively O(0 0 0 0) S1(x1 y1 z1 w1)S2(x2 y2 z2 w2) S3(x3 y3 z3 w3) S4(x4 y4 z4 w4) andS5(x5 y5 z5 w5) -e Jacobian matrix of system (1) atequilibrium point O(0 0 0 0) is of the following form

J0

minus a1 minus a2 a3 a4

minus b1 b2 b3 minus b4

minus c1 minus c2 minus c3 minus c4

d1 minus d2 d3 minus d4

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

So the characteristic polynomial of J(O) is as follows

f(λ) λ4 + Aλ3 + Bλ2 + Cλ + D 0 (5)

where

A a1 minus b2 + c3 + d4

B a3c1 minus a2b1 + b3c2 minus b2c3 minus a4d1 + b4d2 + c4d3 minus b2d4 + c3d4 + a1 c3 + d4 minus b2( 1113857

C a1b3c2 minus a1b2c3 + a4b2d1 minus a4c3d1 minus a4b1d2 + a1b4d2 + b4c3d2 minus b3c4d2

+ a4c1d3 + b4c2d3 + a1c4d3 minus b2c4d3 minus a1b2d4 + b3c2d4 + a1c3d4 minus b2c3d4

+ a3 c4d1 + c1d4 minus b2c1 minus b1c2( 1113857 minus a2 b3c1 minus b4d1 + b1 c3 + d4( 1113857( 1113857

D a2b4c3d1 minus a2b3c4d1 + a1b4c3d2 minus a1b3c4d2 minus a2b4c1d3 + a1b4c2d3 minus a2b1c4d3 minus a1b2c4d3

minus a4 b3c2d1 minus b2c3d1 + b3c1d2 + b1c3d2 + b2c1d3 + b1c2d3( 1113857 minus a2b3c1d4 + a1b3c2d4

minus a2b1c3d4 minus a1b2c3d4 + a3 b4c2d1 minus b2c4d1 + b4c1d2 + b1c4d2 minus b2c1d4 minus b1c2d4( 1113857

(6)

System (1) is a very complex dynamic system when ai bici di M F E N H and P values are different system (1)performance is complex and dynamic behavior is alsodifferent In this study we set the followinga1 009a2 0025 a3 0012 a4 0165 b1 0422 b2 02b3 08 b4 04 c1 0035 c2 0008 c3 0075c4 0078 d1 0121 d2 0035 d3 00145 d4 0775M 09 F 16 E 295 N 035 H 125 and P 24

By calculation four eigenvalues of the Jacobian matrixJ(O) are λ1 02236 λ2 minus 07845 andλ34 minus 00895 plusmn 00706i Because λi lt 1(i 1 2 3 4) weknow that the equilibrium O(0 0 0 0) is unstable

Let c2 be any value so we can obtain the followingcharacteristic equation

f(λ) λ4 + 074λ3 + 08c2 minus 00683( 1113857λ2

+ 06927c2 minus 00297( 1113857λ minus 00026 + 0036c2 0

(7)

Let p1 074 p2 08c2 minus 00683p3 06927c2 minus 00297 and p4 0036c2 minus 00026According to the Routh-Hurwitz criterion we can obtain thefollowing conditions p1 074gt 0 p1p2 minus p3 gt 0 andp1p2p3 minus p4p

21 minus p2

3 gt 0 By calculation when

4 Complexity

0lt c2 lt 00575 that equilibrium point O(0 0 0 0) isunstable

Now bring the parameter values set above to system (1)By calculation we get the equilibrium pointsS1(minus 14149 0534 37951 minus 05030) S2(135 05868

14901 02367) S3(10838 06617 07819 02)S4(08185 25042 07327 minus 04697) andS5(12523 25109 22876 minus 10085) A similar approachshows the eigenvalue of the equilibrium point S1λ1 minus 07309 λ2 minus 04548 and λ34 02696 plusmn 02758i theeigenvalue of the equilibrium point S2λ1 minus 00314λ2 00665 and λ34 minus 00783 plusmn 01974i the eigenvalue ofthe equilibrium point S3λ1 minus 05057 λ2 minus 00189 andλ34 02068 plusmn 03074i the eigenvalue of the equilibriumpoint S4λ1 00232 λ2 01221 andλ34 minus 01191 plusmn 00801i the eigenvalue of the equilibriumpoint S5 λ1 minus 03009 λ2 01127 andλ34 00519 plusmn 01578i At the equilibrium pointS1(minus 14149 0534 37951 minus 05030) 37951 minus 05030) x(t) isnegative and energy intensity is about 014 Environmentalquality w(t) has reached dynamic equilibrium or graduallyimproved which is an ideal state

nablaV z _x

zx+

z _y

zy+

z _z

zz+

z _w

zw minus 1 +

y

M1113874 1113875a1 +

(F minus 2y)b2

F

minus c3 + minus 1 +y

P1113874 1113875d4

b2 minus a1 minus c3 minus d4 + ya1

Mminus2b2

F+

d4

P1113888 1113889

(8)

When (a1M) minus (2b2F) + (d4P) 0 andb2 minus a1 minus c3 minus d4 lt 0 system (1) is dissipative

22 System Simulation Analysis Numerical simulationanalysis of the system allows us to more intuitively see thecomplex dynamic behavior of the system which plays a veryimportant role in the evolution and stability of the researchsystem Next we will carry out dynamic simulation analysisof the 3E system under the energy reduction constraint andselect the initial value of the system [0015 0758 183 15]

As can be seen from Figure 1 the evolution trajectory ofthe system (1) enters an irregular chaotic state and the shapeof the three-dimensional attractor diagram composed ofdifferent parameters is also different

In addition Figure 2 gives system (1) mixed phase di-agram of a two-dimensional plane in different sections Itcan be seen from Figure 2 that the irregular evolutiontrajectories of system (1) under different cross sections arenot the same which also shows that the chaotic motion isirregular and disordered -e generation of mixed behaviorin the 3E system will have a great impact on the stability ofthe system and also cause problems in the normal operationof the system -e time series diagram of system (1) (x(t)y(t) z(t) and w(t)) is given in Figure 3

Figure 4 shows bifurcation diagram and correspondingLyapunov exponential diagram of the variablec2 isin [0006 0014] change of the four-dimensional system(1) From Figure 4 we find that the four-dimensional system(1) has very complex dynamic behavior As we all know theLyapunov exponential is generally used to determinewhether the system is stable If the maximum Lyapunovexponent of the system is greater than 0 it can be explainedthat the system produces mixed chaotic behavior which is afull manifestation of unstable evolution In this study thedegree of complexity of the four-dimensional 3E systemsunder the constraints of energy reduction is self-evident Ifthe maximum Lyapunov exponent of the system is greater

Table 1 -e specific meanings of each parameter are explained

Parameter Explanation (t isin I I is an economic cycle)a1 -e development coefficient of energy saving and emission reduction x(t)

a2 -e inhibition coefficient of pollution emission y(t) on energy saving and emission reduction x(t)

a3 -e influence coefficient of z(t) input of economic growth on energy saving and emission reduction x(t)

a4 -e influence coefficient of w(t) input of environmental quality on energy saving and emission reduction x(t)

b1 -e influence coefficient of the development of energy saving and emission reduction x(t) on pollution emission y(t)

b2 -e development rate elasticity coefficient of pollution emission y(t)

b3 -e influence coefficient of economic growth z(t) on pollution emission y(t)

b4 -e inhibition coefficient of environmental quality w(t) on pollution emission y(t)

c1 -e influence coefficient of the development of energy saving and emission reduction x(t) on economic growthc2 -e influence coefficient of pollution emission y(t) on economic growth z(t)

c3 -e restraint factor of investment in energy saving and emission reduction x(t) on economic growth z(t)

c4 -e restraint factor of investment in improving environmental quality w(t) on economic growth z(t)

d1-e influence coefficient of the development of energy saving and emission reduction x(t) on the improvement of

environmental quality w(t)

d2 -e inhibition coefficient of pollution emission y(t) on environmental quality w(t)

d3 -e influence coefficient of economic growth z(t)rsquos investment on improving environmental quality w(t)

d4 -e speed coefficient of ecological environment self-repair without external interventionM -e peak value of the impact of pollution emission y(t) on energy saving and emission reduction x(t)

F -e peak value of pollution emission y(t) in an economic cycleE -e peak value of economic growth z(t) in an economic cycleN -e peak value of the impact of energy saving and emission reduction x(t) on economic growth z(t) in an economic cycleH -e peak value of the impact of economic growth z(t) on environmental quality w(t) in an economic cycleP -e maximum amount of pollution that can be contained by the ecological environment

Complexity 5

than or equal to zero we can determine the occurrence ofbifurcation in the four-dimensional system Behavior ismore likely to develop into a chaotic trend

Impact of initial state on the evolution trend of thecomplex four-dimensional dynamical system (1) Figure 5shows the sensitive dependence of complex four-dimensional

2

1z

15

y1 1

x

2

0 0

(a)

02

05w

15

1

z 1x

15

10

(b)

02

05

2

w

15

1

z y

15

110

(c)

02

05w

1

y1 1

x

15

0 0

(d)

Figure 1 -ree-dimensional spatial chaotic attractor phase diagram of system (1)

y

0

05

1

15

2

05 1 150x

(a)

z

05

1

15

2

05 1 150x

(b)

w

0

05

1

15

05 1 150x

(c)

z

05

1

15

2

1 20y

(d)

w

0

05

1

15

1 20y

(e)

w

0

05

1

15

1 15 205z

(f )

Figure 2 Two-dimensional plane chaotic attractor phase diagram of system (1)

6 Complexity

system (1) on initial conditions -e sensitivity of system(when losing stability) with (x y z w) (0015 0758

18315) (x1 y z w) (0014 0758 18315) and(x2 y z w) (0016 0758 18315) and a small change inthe initial conditions may cause a large change in the wholefour-dimensional system which indicates that the system issensitive to the initial state From Figure 5 we can also knowthat the initial values vary greatly in the trajectories of thedeviated system (1) Although the initial states are indistin-guishable the initial values will be quickly established afterseveral iterations which is also an important symbol ofchaotic motion

3 System Parameter Identification

31 Data Gathering On the basis of complex interactions afour-dimensional dynamic system that integrates restrictsand promotes energy conservation energy economy andenvironment is established In this study the determination ofthe parameters of the four-dimensional dynamic system is ofgreat significance to the actual research Because the envi-ronment energy intensity and economic growth are affectedby the changes of these variables based on the official statisticsand measured data of the China Statistical Yearbook geneticoptimization of the optimized LM-BP neural networkmethod

x

y

z

w

0

1

2

02 04 06 08 1 12 14 16 180 2t (103)

ndash10123

02 04 06 08 1 12 14 16 18 20t (103)

115

2

02 04 06 08 1 12 14 16 18 20t (103)

0

1

02 04 06 08 1 12 14 16 18 20t (103)

Figure 3 System (1) time sequences diagram

y

08

1

12

14

16

18

0008 001 0012 00140006c2

(a)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Lyap

unov

expo

nent

s

0008 001 0012 00140006c2

(b)

Figure 4 With c2 isin [0006 0014] change system (1) (a) bifurcation diagram (b) Lyapunov exponential diagram of corresponding (a)

Complexity 7

is used to obtain the actual parameters of the four-dimen-sional system to further analyze the evolutionary relationshipbetween energy consumption energy economic growth andthe environment of the 3E system

In this paper we mainly use the calculation method ofenergy reduction that is now common in the world tocalculate the amount of skill emission reduction [18] -eprincipal component analysis method based on the co-variance matrix is used to calculate the environmentalquality index [1] to represent the data of the environmentalchange Data on energy consumption and economic growthare mainly derived from Chinarsquos official statistical yearbookIn addition in order to make the environmental qualityindex positive during the research process we also use thelogarithmic logic model for data standardization All thedata in Table 2 is a standardized process based on the 1999data -e final data is as follows

32 Model Validation -e LM-BP neural network methodoptimized by genetic algorithm has a good application in theparameter identification of nonlinear systems [1] and it hasgood identification accuracy which makes this methodwidely used in nonidentification of linear system parame-ters After system (1) is discretized the difference equation ofthe following form is obtained

x(k + 1) x(k) + T a1x(k)y

M minus 11113874 1113875 minus a2y + a3z + a4w1113876 1113877

y(k + 1) y(k) + T minus b1x + b2y1 minus y

F1113874 1113875 + b3z

1 minus z

E1113874 1113875 minus b4w1113876 1113877

z(k + 1) z(k) + T c1xx

N minus 11113874 1113875 minus c2y minus c3z minus c4w1113876 1113877

w(k + 1) w(k) + T d1x minus d2y + d3z1 minus z

H1113874 1113875 + d4w

y

P minus 11113874 11138751113876 1113877

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

In this study we used the former n minus 1 group of data asthe input data of the LM-BP neural network optimized bythe genetic algorithm and the post n minus 1 data as the outputdata of the LM-BP neural network optimized by the geneticalgorithm In addition the data needs to be normalized inxi (xi minus xmin)(xmax minus xmin) form All other parameterswill be set to random number and the identified errorcontrol 10minus 6 Finally the identified system parametersare asshown in Table 3

-e data of 1980 is selected as the initial value of system[000000085 0658 173 11211] and the true validity of theidentification parameters is further verified -e evolutiontrajectory of the system is shown in Figures 6 and 7 It can beseen from the phase diagram of the evolutionary trajectoryof the system that the evolution trajectory of the system ismulticycle and can always be in a stable mode -is explainsthe true effectiveness of the system from the side which isalso in line with the real situation

4 System Parameter Analysis

In order to fully understand the stability of the above four-dimensional system (1) as well as the changes and impacts ofenergy intensity how to effectively reduce energy intensitystabilize economic development improve the quality ofecological environment and seek for high-quality sus-tainable development models and strategies and suggestionsfor the coordinated development of energy economy andenvironment therefore it is necessary to conduct an in-depth analysis of some key parameters of the four-dimen-sional system (1)

In Figures 8(a) and 8(b) we can find that althoughincreasing the investment in energy saving and emissionreduction can effectively improve the environmental qualitythe effect on reducing energy intensity is not obvious Overtime the amplitudes of the evolutionary fluctuations ofenergy intensity and environmental quality oscillate around

0

02

04

06

08

1

12

14

16

Erro

r sta

rtin

g fro

m d

iffer

ent i

nitia

l con

ditio

ns

05 2 3 45351 415 25 50t (103)

x (x = 0016)x (x = 0015)x (x = 0014)

Figure 5 System (1) sensitivity analysis

Table 2 Statistics on energy reduction energy consumption GDPand environment in China

Year x y z w

2000 19626 10455 11085 098372001 36786 11066 12228 095952002 22791 12064 13482 093472003 12699 14020 15283 087472004 23033 16382 18062 077412005 19352 18594 20813 072422006 20778 20380 24509 064032007 39437 22156 30307 054552008 65583 22808 35976 047522009 32830 23912 38997 040612010 33307 25656 46020 036932011 36871 27534 54243 035652012 40130 28608 60326 032102013 39274 29659 66068 028172014 42167 30292 72151 025752015 42893 30583 76813 023222016 45925 31004 82872 021592017 46121 31942 92297 02147

8 Complexity

Tabl

e3

System

(1)identifi

estheactual

parameters

a1

a2

a3

a4

b1

b2

b3

b4

c 1c 2

c 3c 4

d1

d2

d3

d4

MF

EN

HP

01277

02338

01992

00115

01896

04325

03818

00141

07582

05265

05834

00534

00591

00191

02567

05892

06523

05816

06437

05573

06943

07121

Complexity 9

a certain value In a relatively short period of time theimprovement of environmental quality is also very obviousbut in the long run the environment is still deteriorating

with the decline in the discount rate of energy-saving andemission-reduction inputs -e oscillating amplitude ofenergy intensity will decrease significantly with the increase

2

1

008

0604

02ndash04

0y x

z

(a)

ndash040

x

w

z

1

05

0

ndash052

10

(b)

1

05

0

ndash05

w

z y

21

0 0204

0608

(c)

1

05

0

ndash05

w

0806

0402y ndash04

0x

(d)

Figure 6 -ree-dimensional spatial phase diagram of system (1) with identified parameters

08

06

04

02

y

xndash04ndash06 ndash02 0

(a)

2

1

0

z

xndash04 ndash02ndash06 0

(b)

w

xndash04 ndash02ndash06 0

1

0

ndash1

(c)

2

1

0

02 04 06 08

z

y

(d)

02 04 06 08y

w

1

0

ndash1

(e)

z

w

1

0

ndash10 1 2

(f )

Figure 7 Two-dimensional plane phase diagram of system (1) with identified parameters

10 Complexity

of energy-saving and emission-reduction input but there isno obvious effect on the peak energy intensity -erefore itis not obvious that the effect of reducing the energy intensityand improving the stability of environmental quality bysimply increasing the investment in energy saving andemission reduction is not obvious

From Figures 9(a) and 9(b) we can find that when thepeak value of pollution emissions F 05816 the evolutiontrajectories of energy intensity and environmental qualityshow fluctuations around a certain central value over time-is phenomenon will be very unfavorable to the im-provement of environmental quality in controlling pollutionemissions (ie the inability to effectively reflect the energyreduction policies) when F 04816 with the passage oftime energy intensity and environmental quality are stillfluctuating up and down at a certain central value but willgradually shrink with the magnitude of evolutionary fluc-tuations and the maximum peak of energy intensity is alsosignificantly smaller than before It also has a significantimpact on the evolution of environmental quality In thelong run the central value of the shock is decreasing theamplitude of the shock is decreasing and eventually it tendsto be stable After the pollution emission peak is loweredagain F 03816 the energy intensity and environmentalquality evolve to a stable value at a relatively fast rate and thepeak value of the energy intensity and the center value of theoscillation are reduced again before comparison -ereforeit can be better explained that effective control of the peakarrival time of pollution emissions can be used as an im-portant decision for pollution emission control and energyintensity reduction

From Figure 9(b) we can also find that the advance ofthe peak of pollution emissions makes the environmentalsystem take the risk ahead and the threat level is greatlyincreased -e reason for this phenomenon is that the peakof pollution discharge exceeds the self-purification speed ofthe natural environment system during the self-circulationprocess so that the accumulation of pollutants in the eco-logical environment system reaches the maximum capacityand the self-purification ability of the environmental system

is weakened In a relatively short period of time the eco-logical environment system is extremely deteriorated-erefore how to effectively and reasonably control the peakof pollution emission is very important for controlling thestability of 3E system and improving the environmentalquality

By comparing Figure 10(a) it can be found that in theshort term the environmental capacity of the ecosystem hasno significant effect on the stability of the evolution of the 3Esystem As the environmental capacity decreases over timethe evolution of environmental quality shows an upwardtrend of fluctuations and fluctuations around a certaincentral value when the capacity of the ecosystem falls to thelimit (ie the pollution effect exceeds the ecological envi-ronment) the system collapses (ie the ecological envi-ronment disappears and the ecosystem can no longer relyon self-regulation to repair the ecological environment) As aresult this situation continues and the ecological environ-ment is eventually sold out It is confirmed that the eco-logical environment system has a certain bearing capacityand the effect that the ecosystem will not be in operation orself-purification after the limit value can be exceeded is notsignificant

From Figure 10(b) we can find that the effect of simplyincreasing the economic investment in the environment toimprove the environmental quality is not obvious it doesnot increase the economic investment as expected and theenvironment can be effectively improved From the evolu-tionary trajectory of the system it can be seen that theevolutionary trajectory of the system revolves around centralvalue fluctuation and oscillation amplitude over time -isphenomenon shows that the effects of economic input in theprocess of environmental governance are not significantenough -erefore in order to improve the quality of theecological environment and promote the rapid developmentof the economy we need more measures to use more meansand technologies to promote stable economic growth andmanagement of the ecological environment It is necessaryto correctly grasp the ecological environment protection andthe relationship between economic developments explore

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash4

ndash3

ndash2

ndash1

0

1

2

Envi

ronm

enta

l qua

lity

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

(b)

Figure 8 -e parameters a3 on the influence of system (1)

Complexity 11

synergies to promote ecological priorities and green de-velopment new ideas and ultimately achieve a ldquowin-winrdquoenvironment and economy

5 Conclusion

In this study the energy economic and environmental (3E)four-dimensional system model of energy conservationconstraints was first established -e Bayesian estimationmethod is used to correct the environmental quality vari-ables to obtain the environmental quality data needed for theresearch In addition based on the Chinese statisticalyearbook data the LevenbergndashMarquardt BP neural net-work method optimized by genetic algorithm is used toenergy economy and environment under energy conser-vation constraints -e parameters in the four-dimensionalsystem model are effectively identified Finally the systemscience analysis theory and complex system dynamics theoryare used to analyze the stability and complex dynamics of the

model and explore the influence of some key parameters inthe four-dimensional system on the evolution stability of thesystem -e main conclusions are as follows

(1) Although increasing the investment in energy re-duction can effectively improve the environmentalquality in a relatively short period of time theimprovement of environmental quality is also veryobvious but in the long run the environment is stilldeteriorating with the decline in the discount rate ofenergy reduction inputs

(2) It can be better explained that effective control of thepeak arrival time of pollution emissions can be usedas an important decision for pollution emissioncontrol and energy intensity reduction thereforehow to effectively and reasonably control the peak ofpollution emissions is of great significance forcontrolling the stability of energy economy andenvironment system under the constraint of energy

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

(b)

Figure 9 -e parameters F on the influence of system (1)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redP = 05121 blue P = 06121 and green

P = 07121)

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redd3 = 02667 blue d3 = 03667 and green

d3 = 04667)

(b)

Figure 10 -e different parameters P and d3 on the influence of system (1)

12 Complexity

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

0lt c2 lt 00575 that equilibrium point O(0 0 0 0) isunstable

Now bring the parameter values set above to system (1)By calculation we get the equilibrium pointsS1(minus 14149 0534 37951 minus 05030) S2(135 05868

14901 02367) S3(10838 06617 07819 02)S4(08185 25042 07327 minus 04697) andS5(12523 25109 22876 minus 10085) A similar approachshows the eigenvalue of the equilibrium point S1λ1 minus 07309 λ2 minus 04548 and λ34 02696 plusmn 02758i theeigenvalue of the equilibrium point S2λ1 minus 00314λ2 00665 and λ34 minus 00783 plusmn 01974i the eigenvalue ofthe equilibrium point S3λ1 minus 05057 λ2 minus 00189 andλ34 02068 plusmn 03074i the eigenvalue of the equilibriumpoint S4λ1 00232 λ2 01221 andλ34 minus 01191 plusmn 00801i the eigenvalue of the equilibriumpoint S5 λ1 minus 03009 λ2 01127 andλ34 00519 plusmn 01578i At the equilibrium pointS1(minus 14149 0534 37951 minus 05030) 37951 minus 05030) x(t) isnegative and energy intensity is about 014 Environmentalquality w(t) has reached dynamic equilibrium or graduallyimproved which is an ideal state

nablaV z _x

zx+

z _y

zy+

z _z

zz+

z _w

zw minus 1 +

y

M1113874 1113875a1 +

(F minus 2y)b2

F

minus c3 + minus 1 +y

P1113874 1113875d4

b2 minus a1 minus c3 minus d4 + ya1

Mminus2b2

F+

d4

P1113888 1113889

(8)

When (a1M) minus (2b2F) + (d4P) 0 andb2 minus a1 minus c3 minus d4 lt 0 system (1) is dissipative

22 System Simulation Analysis Numerical simulationanalysis of the system allows us to more intuitively see thecomplex dynamic behavior of the system which plays a veryimportant role in the evolution and stability of the researchsystem Next we will carry out dynamic simulation analysisof the 3E system under the energy reduction constraint andselect the initial value of the system [0015 0758 183 15]

As can be seen from Figure 1 the evolution trajectory ofthe system (1) enters an irregular chaotic state and the shapeof the three-dimensional attractor diagram composed ofdifferent parameters is also different

In addition Figure 2 gives system (1) mixed phase di-agram of a two-dimensional plane in different sections Itcan be seen from Figure 2 that the irregular evolutiontrajectories of system (1) under different cross sections arenot the same which also shows that the chaotic motion isirregular and disordered -e generation of mixed behaviorin the 3E system will have a great impact on the stability ofthe system and also cause problems in the normal operationof the system -e time series diagram of system (1) (x(t)y(t) z(t) and w(t)) is given in Figure 3

Figure 4 shows bifurcation diagram and correspondingLyapunov exponential diagram of the variablec2 isin [0006 0014] change of the four-dimensional system(1) From Figure 4 we find that the four-dimensional system(1) has very complex dynamic behavior As we all know theLyapunov exponential is generally used to determinewhether the system is stable If the maximum Lyapunovexponent of the system is greater than 0 it can be explainedthat the system produces mixed chaotic behavior which is afull manifestation of unstable evolution In this study thedegree of complexity of the four-dimensional 3E systemsunder the constraints of energy reduction is self-evident Ifthe maximum Lyapunov exponent of the system is greater

Table 1 -e specific meanings of each parameter are explained

Parameter Explanation (t isin I I is an economic cycle)a1 -e development coefficient of energy saving and emission reduction x(t)

a2 -e inhibition coefficient of pollution emission y(t) on energy saving and emission reduction x(t)

a3 -e influence coefficient of z(t) input of economic growth on energy saving and emission reduction x(t)

a4 -e influence coefficient of w(t) input of environmental quality on energy saving and emission reduction x(t)

b1 -e influence coefficient of the development of energy saving and emission reduction x(t) on pollution emission y(t)

b2 -e development rate elasticity coefficient of pollution emission y(t)

b3 -e influence coefficient of economic growth z(t) on pollution emission y(t)

b4 -e inhibition coefficient of environmental quality w(t) on pollution emission y(t)

c1 -e influence coefficient of the development of energy saving and emission reduction x(t) on economic growthc2 -e influence coefficient of pollution emission y(t) on economic growth z(t)

c3 -e restraint factor of investment in energy saving and emission reduction x(t) on economic growth z(t)

c4 -e restraint factor of investment in improving environmental quality w(t) on economic growth z(t)

d1-e influence coefficient of the development of energy saving and emission reduction x(t) on the improvement of

environmental quality w(t)

d2 -e inhibition coefficient of pollution emission y(t) on environmental quality w(t)

d3 -e influence coefficient of economic growth z(t)rsquos investment on improving environmental quality w(t)

d4 -e speed coefficient of ecological environment self-repair without external interventionM -e peak value of the impact of pollution emission y(t) on energy saving and emission reduction x(t)

F -e peak value of pollution emission y(t) in an economic cycleE -e peak value of economic growth z(t) in an economic cycleN -e peak value of the impact of energy saving and emission reduction x(t) on economic growth z(t) in an economic cycleH -e peak value of the impact of economic growth z(t) on environmental quality w(t) in an economic cycleP -e maximum amount of pollution that can be contained by the ecological environment

Complexity 5

than or equal to zero we can determine the occurrence ofbifurcation in the four-dimensional system Behavior ismore likely to develop into a chaotic trend

Impact of initial state on the evolution trend of thecomplex four-dimensional dynamical system (1) Figure 5shows the sensitive dependence of complex four-dimensional

2

1z

15

y1 1

x

2

0 0

(a)

02

05w

15

1

z 1x

15

10

(b)

02

05

2

w

15

1

z y

15

110

(c)

02

05w

1

y1 1

x

15

0 0

(d)

Figure 1 -ree-dimensional spatial chaotic attractor phase diagram of system (1)

y

0

05

1

15

2

05 1 150x

(a)

z

05

1

15

2

05 1 150x

(b)

w

0

05

1

15

05 1 150x

(c)

z

05

1

15

2

1 20y

(d)

w

0

05

1

15

1 20y

(e)

w

0

05

1

15

1 15 205z

(f )

Figure 2 Two-dimensional plane chaotic attractor phase diagram of system (1)

6 Complexity

system (1) on initial conditions -e sensitivity of system(when losing stability) with (x y z w) (0015 0758

18315) (x1 y z w) (0014 0758 18315) and(x2 y z w) (0016 0758 18315) and a small change inthe initial conditions may cause a large change in the wholefour-dimensional system which indicates that the system issensitive to the initial state From Figure 5 we can also knowthat the initial values vary greatly in the trajectories of thedeviated system (1) Although the initial states are indistin-guishable the initial values will be quickly established afterseveral iterations which is also an important symbol ofchaotic motion

3 System Parameter Identification

31 Data Gathering On the basis of complex interactions afour-dimensional dynamic system that integrates restrictsand promotes energy conservation energy economy andenvironment is established In this study the determination ofthe parameters of the four-dimensional dynamic system is ofgreat significance to the actual research Because the envi-ronment energy intensity and economic growth are affectedby the changes of these variables based on the official statisticsand measured data of the China Statistical Yearbook geneticoptimization of the optimized LM-BP neural networkmethod

x

y

z

w

0

1

2

02 04 06 08 1 12 14 16 180 2t (103)

ndash10123

02 04 06 08 1 12 14 16 18 20t (103)

115

2

02 04 06 08 1 12 14 16 18 20t (103)

0

1

02 04 06 08 1 12 14 16 18 20t (103)

Figure 3 System (1) time sequences diagram

y

08

1

12

14

16

18

0008 001 0012 00140006c2

(a)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Lyap

unov

expo

nent

s

0008 001 0012 00140006c2

(b)

Figure 4 With c2 isin [0006 0014] change system (1) (a) bifurcation diagram (b) Lyapunov exponential diagram of corresponding (a)

Complexity 7

is used to obtain the actual parameters of the four-dimen-sional system to further analyze the evolutionary relationshipbetween energy consumption energy economic growth andthe environment of the 3E system

In this paper we mainly use the calculation method ofenergy reduction that is now common in the world tocalculate the amount of skill emission reduction [18] -eprincipal component analysis method based on the co-variance matrix is used to calculate the environmentalquality index [1] to represent the data of the environmentalchange Data on energy consumption and economic growthare mainly derived from Chinarsquos official statistical yearbookIn addition in order to make the environmental qualityindex positive during the research process we also use thelogarithmic logic model for data standardization All thedata in Table 2 is a standardized process based on the 1999data -e final data is as follows

32 Model Validation -e LM-BP neural network methodoptimized by genetic algorithm has a good application in theparameter identification of nonlinear systems [1] and it hasgood identification accuracy which makes this methodwidely used in nonidentification of linear system parame-ters After system (1) is discretized the difference equation ofthe following form is obtained

x(k + 1) x(k) + T a1x(k)y

M minus 11113874 1113875 minus a2y + a3z + a4w1113876 1113877

y(k + 1) y(k) + T minus b1x + b2y1 minus y

F1113874 1113875 + b3z

1 minus z

E1113874 1113875 minus b4w1113876 1113877

z(k + 1) z(k) + T c1xx

N minus 11113874 1113875 minus c2y minus c3z minus c4w1113876 1113877

w(k + 1) w(k) + T d1x minus d2y + d3z1 minus z

H1113874 1113875 + d4w

y

P minus 11113874 11138751113876 1113877

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

In this study we used the former n minus 1 group of data asthe input data of the LM-BP neural network optimized bythe genetic algorithm and the post n minus 1 data as the outputdata of the LM-BP neural network optimized by the geneticalgorithm In addition the data needs to be normalized inxi (xi minus xmin)(xmax minus xmin) form All other parameterswill be set to random number and the identified errorcontrol 10minus 6 Finally the identified system parametersare asshown in Table 3

-e data of 1980 is selected as the initial value of system[000000085 0658 173 11211] and the true validity of theidentification parameters is further verified -e evolutiontrajectory of the system is shown in Figures 6 and 7 It can beseen from the phase diagram of the evolutionary trajectoryof the system that the evolution trajectory of the system ismulticycle and can always be in a stable mode -is explainsthe true effectiveness of the system from the side which isalso in line with the real situation

4 System Parameter Analysis

In order to fully understand the stability of the above four-dimensional system (1) as well as the changes and impacts ofenergy intensity how to effectively reduce energy intensitystabilize economic development improve the quality ofecological environment and seek for high-quality sus-tainable development models and strategies and suggestionsfor the coordinated development of energy economy andenvironment therefore it is necessary to conduct an in-depth analysis of some key parameters of the four-dimen-sional system (1)

In Figures 8(a) and 8(b) we can find that althoughincreasing the investment in energy saving and emissionreduction can effectively improve the environmental qualitythe effect on reducing energy intensity is not obvious Overtime the amplitudes of the evolutionary fluctuations ofenergy intensity and environmental quality oscillate around

0

02

04

06

08

1

12

14

16

Erro

r sta

rtin

g fro

m d

iffer

ent i

nitia

l con

ditio

ns

05 2 3 45351 415 25 50t (103)

x (x = 0016)x (x = 0015)x (x = 0014)

Figure 5 System (1) sensitivity analysis

Table 2 Statistics on energy reduction energy consumption GDPand environment in China

Year x y z w

2000 19626 10455 11085 098372001 36786 11066 12228 095952002 22791 12064 13482 093472003 12699 14020 15283 087472004 23033 16382 18062 077412005 19352 18594 20813 072422006 20778 20380 24509 064032007 39437 22156 30307 054552008 65583 22808 35976 047522009 32830 23912 38997 040612010 33307 25656 46020 036932011 36871 27534 54243 035652012 40130 28608 60326 032102013 39274 29659 66068 028172014 42167 30292 72151 025752015 42893 30583 76813 023222016 45925 31004 82872 021592017 46121 31942 92297 02147

8 Complexity

Tabl

e3

System

(1)identifi

estheactual

parameters

a1

a2

a3

a4

b1

b2

b3

b4

c 1c 2

c 3c 4

d1

d2

d3

d4

MF

EN

HP

01277

02338

01992

00115

01896

04325

03818

00141

07582

05265

05834

00534

00591

00191

02567

05892

06523

05816

06437

05573

06943

07121

Complexity 9

a certain value In a relatively short period of time theimprovement of environmental quality is also very obviousbut in the long run the environment is still deteriorating

with the decline in the discount rate of energy-saving andemission-reduction inputs -e oscillating amplitude ofenergy intensity will decrease significantly with the increase

2

1

008

0604

02ndash04

0y x

z

(a)

ndash040

x

w

z

1

05

0

ndash052

10

(b)

1

05

0

ndash05

w

z y

21

0 0204

0608

(c)

1

05

0

ndash05

w

0806

0402y ndash04

0x

(d)

Figure 6 -ree-dimensional spatial phase diagram of system (1) with identified parameters

08

06

04

02

y

xndash04ndash06 ndash02 0

(a)

2

1

0

z

xndash04 ndash02ndash06 0

(b)

w

xndash04 ndash02ndash06 0

1

0

ndash1

(c)

2

1

0

02 04 06 08

z

y

(d)

02 04 06 08y

w

1

0

ndash1

(e)

z

w

1

0

ndash10 1 2

(f )

Figure 7 Two-dimensional plane phase diagram of system (1) with identified parameters

10 Complexity

of energy-saving and emission-reduction input but there isno obvious effect on the peak energy intensity -erefore itis not obvious that the effect of reducing the energy intensityand improving the stability of environmental quality bysimply increasing the investment in energy saving andemission reduction is not obvious

From Figures 9(a) and 9(b) we can find that when thepeak value of pollution emissions F 05816 the evolutiontrajectories of energy intensity and environmental qualityshow fluctuations around a certain central value over time-is phenomenon will be very unfavorable to the im-provement of environmental quality in controlling pollutionemissions (ie the inability to effectively reflect the energyreduction policies) when F 04816 with the passage oftime energy intensity and environmental quality are stillfluctuating up and down at a certain central value but willgradually shrink with the magnitude of evolutionary fluc-tuations and the maximum peak of energy intensity is alsosignificantly smaller than before It also has a significantimpact on the evolution of environmental quality In thelong run the central value of the shock is decreasing theamplitude of the shock is decreasing and eventually it tendsto be stable After the pollution emission peak is loweredagain F 03816 the energy intensity and environmentalquality evolve to a stable value at a relatively fast rate and thepeak value of the energy intensity and the center value of theoscillation are reduced again before comparison -ereforeit can be better explained that effective control of the peakarrival time of pollution emissions can be used as an im-portant decision for pollution emission control and energyintensity reduction

From Figure 9(b) we can also find that the advance ofthe peak of pollution emissions makes the environmentalsystem take the risk ahead and the threat level is greatlyincreased -e reason for this phenomenon is that the peakof pollution discharge exceeds the self-purification speed ofthe natural environment system during the self-circulationprocess so that the accumulation of pollutants in the eco-logical environment system reaches the maximum capacityand the self-purification ability of the environmental system

is weakened In a relatively short period of time the eco-logical environment system is extremely deteriorated-erefore how to effectively and reasonably control the peakof pollution emission is very important for controlling thestability of 3E system and improving the environmentalquality

By comparing Figure 10(a) it can be found that in theshort term the environmental capacity of the ecosystem hasno significant effect on the stability of the evolution of the 3Esystem As the environmental capacity decreases over timethe evolution of environmental quality shows an upwardtrend of fluctuations and fluctuations around a certaincentral value when the capacity of the ecosystem falls to thelimit (ie the pollution effect exceeds the ecological envi-ronment) the system collapses (ie the ecological envi-ronment disappears and the ecosystem can no longer relyon self-regulation to repair the ecological environment) As aresult this situation continues and the ecological environ-ment is eventually sold out It is confirmed that the eco-logical environment system has a certain bearing capacityand the effect that the ecosystem will not be in operation orself-purification after the limit value can be exceeded is notsignificant

From Figure 10(b) we can find that the effect of simplyincreasing the economic investment in the environment toimprove the environmental quality is not obvious it doesnot increase the economic investment as expected and theenvironment can be effectively improved From the evolu-tionary trajectory of the system it can be seen that theevolutionary trajectory of the system revolves around centralvalue fluctuation and oscillation amplitude over time -isphenomenon shows that the effects of economic input in theprocess of environmental governance are not significantenough -erefore in order to improve the quality of theecological environment and promote the rapid developmentof the economy we need more measures to use more meansand technologies to promote stable economic growth andmanagement of the ecological environment It is necessaryto correctly grasp the ecological environment protection andthe relationship between economic developments explore

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash4

ndash3

ndash2

ndash1

0

1

2

Envi

ronm

enta

l qua

lity

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

(b)

Figure 8 -e parameters a3 on the influence of system (1)

Complexity 11

synergies to promote ecological priorities and green de-velopment new ideas and ultimately achieve a ldquowin-winrdquoenvironment and economy

5 Conclusion

In this study the energy economic and environmental (3E)four-dimensional system model of energy conservationconstraints was first established -e Bayesian estimationmethod is used to correct the environmental quality vari-ables to obtain the environmental quality data needed for theresearch In addition based on the Chinese statisticalyearbook data the LevenbergndashMarquardt BP neural net-work method optimized by genetic algorithm is used toenergy economy and environment under energy conser-vation constraints -e parameters in the four-dimensionalsystem model are effectively identified Finally the systemscience analysis theory and complex system dynamics theoryare used to analyze the stability and complex dynamics of the

model and explore the influence of some key parameters inthe four-dimensional system on the evolution stability of thesystem -e main conclusions are as follows

(1) Although increasing the investment in energy re-duction can effectively improve the environmentalquality in a relatively short period of time theimprovement of environmental quality is also veryobvious but in the long run the environment is stilldeteriorating with the decline in the discount rate ofenergy reduction inputs

(2) It can be better explained that effective control of thepeak arrival time of pollution emissions can be usedas an important decision for pollution emissioncontrol and energy intensity reduction thereforehow to effectively and reasonably control the peak ofpollution emissions is of great significance forcontrolling the stability of energy economy andenvironment system under the constraint of energy

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

(b)

Figure 9 -e parameters F on the influence of system (1)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redP = 05121 blue P = 06121 and green

P = 07121)

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redd3 = 02667 blue d3 = 03667 and green

d3 = 04667)

(b)

Figure 10 -e different parameters P and d3 on the influence of system (1)

12 Complexity

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

than or equal to zero we can determine the occurrence ofbifurcation in the four-dimensional system Behavior ismore likely to develop into a chaotic trend

Impact of initial state on the evolution trend of thecomplex four-dimensional dynamical system (1) Figure 5shows the sensitive dependence of complex four-dimensional

2

1z

15

y1 1

x

2

0 0

(a)

02

05w

15

1

z 1x

15

10

(b)

02

05

2

w

15

1

z y

15

110

(c)

02

05w

1

y1 1

x

15

0 0

(d)

Figure 1 -ree-dimensional spatial chaotic attractor phase diagram of system (1)

y

0

05

1

15

2

05 1 150x

(a)

z

05

1

15

2

05 1 150x

(b)

w

0

05

1

15

05 1 150x

(c)

z

05

1

15

2

1 20y

(d)

w

0

05

1

15

1 20y

(e)

w

0

05

1

15

1 15 205z

(f )

Figure 2 Two-dimensional plane chaotic attractor phase diagram of system (1)

6 Complexity

system (1) on initial conditions -e sensitivity of system(when losing stability) with (x y z w) (0015 0758

18315) (x1 y z w) (0014 0758 18315) and(x2 y z w) (0016 0758 18315) and a small change inthe initial conditions may cause a large change in the wholefour-dimensional system which indicates that the system issensitive to the initial state From Figure 5 we can also knowthat the initial values vary greatly in the trajectories of thedeviated system (1) Although the initial states are indistin-guishable the initial values will be quickly established afterseveral iterations which is also an important symbol ofchaotic motion

3 System Parameter Identification

31 Data Gathering On the basis of complex interactions afour-dimensional dynamic system that integrates restrictsand promotes energy conservation energy economy andenvironment is established In this study the determination ofthe parameters of the four-dimensional dynamic system is ofgreat significance to the actual research Because the envi-ronment energy intensity and economic growth are affectedby the changes of these variables based on the official statisticsand measured data of the China Statistical Yearbook geneticoptimization of the optimized LM-BP neural networkmethod

x

y

z

w

0

1

2

02 04 06 08 1 12 14 16 180 2t (103)

ndash10123

02 04 06 08 1 12 14 16 18 20t (103)

115

2

02 04 06 08 1 12 14 16 18 20t (103)

0

1

02 04 06 08 1 12 14 16 18 20t (103)

Figure 3 System (1) time sequences diagram

y

08

1

12

14

16

18

0008 001 0012 00140006c2

(a)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Lyap

unov

expo

nent

s

0008 001 0012 00140006c2

(b)

Figure 4 With c2 isin [0006 0014] change system (1) (a) bifurcation diagram (b) Lyapunov exponential diagram of corresponding (a)

Complexity 7

is used to obtain the actual parameters of the four-dimen-sional system to further analyze the evolutionary relationshipbetween energy consumption energy economic growth andthe environment of the 3E system

In this paper we mainly use the calculation method ofenergy reduction that is now common in the world tocalculate the amount of skill emission reduction [18] -eprincipal component analysis method based on the co-variance matrix is used to calculate the environmentalquality index [1] to represent the data of the environmentalchange Data on energy consumption and economic growthare mainly derived from Chinarsquos official statistical yearbookIn addition in order to make the environmental qualityindex positive during the research process we also use thelogarithmic logic model for data standardization All thedata in Table 2 is a standardized process based on the 1999data -e final data is as follows

32 Model Validation -e LM-BP neural network methodoptimized by genetic algorithm has a good application in theparameter identification of nonlinear systems [1] and it hasgood identification accuracy which makes this methodwidely used in nonidentification of linear system parame-ters After system (1) is discretized the difference equation ofthe following form is obtained

x(k + 1) x(k) + T a1x(k)y

M minus 11113874 1113875 minus a2y + a3z + a4w1113876 1113877

y(k + 1) y(k) + T minus b1x + b2y1 minus y

F1113874 1113875 + b3z

1 minus z

E1113874 1113875 minus b4w1113876 1113877

z(k + 1) z(k) + T c1xx

N minus 11113874 1113875 minus c2y minus c3z minus c4w1113876 1113877

w(k + 1) w(k) + T d1x minus d2y + d3z1 minus z

H1113874 1113875 + d4w

y

P minus 11113874 11138751113876 1113877

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

In this study we used the former n minus 1 group of data asthe input data of the LM-BP neural network optimized bythe genetic algorithm and the post n minus 1 data as the outputdata of the LM-BP neural network optimized by the geneticalgorithm In addition the data needs to be normalized inxi (xi minus xmin)(xmax minus xmin) form All other parameterswill be set to random number and the identified errorcontrol 10minus 6 Finally the identified system parametersare asshown in Table 3

-e data of 1980 is selected as the initial value of system[000000085 0658 173 11211] and the true validity of theidentification parameters is further verified -e evolutiontrajectory of the system is shown in Figures 6 and 7 It can beseen from the phase diagram of the evolutionary trajectoryof the system that the evolution trajectory of the system ismulticycle and can always be in a stable mode -is explainsthe true effectiveness of the system from the side which isalso in line with the real situation

4 System Parameter Analysis

In order to fully understand the stability of the above four-dimensional system (1) as well as the changes and impacts ofenergy intensity how to effectively reduce energy intensitystabilize economic development improve the quality ofecological environment and seek for high-quality sus-tainable development models and strategies and suggestionsfor the coordinated development of energy economy andenvironment therefore it is necessary to conduct an in-depth analysis of some key parameters of the four-dimen-sional system (1)

In Figures 8(a) and 8(b) we can find that althoughincreasing the investment in energy saving and emissionreduction can effectively improve the environmental qualitythe effect on reducing energy intensity is not obvious Overtime the amplitudes of the evolutionary fluctuations ofenergy intensity and environmental quality oscillate around

0

02

04

06

08

1

12

14

16

Erro

r sta

rtin

g fro

m d

iffer

ent i

nitia

l con

ditio

ns

05 2 3 45351 415 25 50t (103)

x (x = 0016)x (x = 0015)x (x = 0014)

Figure 5 System (1) sensitivity analysis

Table 2 Statistics on energy reduction energy consumption GDPand environment in China

Year x y z w

2000 19626 10455 11085 098372001 36786 11066 12228 095952002 22791 12064 13482 093472003 12699 14020 15283 087472004 23033 16382 18062 077412005 19352 18594 20813 072422006 20778 20380 24509 064032007 39437 22156 30307 054552008 65583 22808 35976 047522009 32830 23912 38997 040612010 33307 25656 46020 036932011 36871 27534 54243 035652012 40130 28608 60326 032102013 39274 29659 66068 028172014 42167 30292 72151 025752015 42893 30583 76813 023222016 45925 31004 82872 021592017 46121 31942 92297 02147

8 Complexity

Tabl

e3

System

(1)identifi

estheactual

parameters

a1

a2

a3

a4

b1

b2

b3

b4

c 1c 2

c 3c 4

d1

d2

d3

d4

MF

EN

HP

01277

02338

01992

00115

01896

04325

03818

00141

07582

05265

05834

00534

00591

00191

02567

05892

06523

05816

06437

05573

06943

07121

Complexity 9

a certain value In a relatively short period of time theimprovement of environmental quality is also very obviousbut in the long run the environment is still deteriorating

with the decline in the discount rate of energy-saving andemission-reduction inputs -e oscillating amplitude ofenergy intensity will decrease significantly with the increase

2

1

008

0604

02ndash04

0y x

z

(a)

ndash040

x

w

z

1

05

0

ndash052

10

(b)

1

05

0

ndash05

w

z y

21

0 0204

0608

(c)

1

05

0

ndash05

w

0806

0402y ndash04

0x

(d)

Figure 6 -ree-dimensional spatial phase diagram of system (1) with identified parameters

08

06

04

02

y

xndash04ndash06 ndash02 0

(a)

2

1

0

z

xndash04 ndash02ndash06 0

(b)

w

xndash04 ndash02ndash06 0

1

0

ndash1

(c)

2

1

0

02 04 06 08

z

y

(d)

02 04 06 08y

w

1

0

ndash1

(e)

z

w

1

0

ndash10 1 2

(f )

Figure 7 Two-dimensional plane phase diagram of system (1) with identified parameters

10 Complexity

of energy-saving and emission-reduction input but there isno obvious effect on the peak energy intensity -erefore itis not obvious that the effect of reducing the energy intensityand improving the stability of environmental quality bysimply increasing the investment in energy saving andemission reduction is not obvious

From Figures 9(a) and 9(b) we can find that when thepeak value of pollution emissions F 05816 the evolutiontrajectories of energy intensity and environmental qualityshow fluctuations around a certain central value over time-is phenomenon will be very unfavorable to the im-provement of environmental quality in controlling pollutionemissions (ie the inability to effectively reflect the energyreduction policies) when F 04816 with the passage oftime energy intensity and environmental quality are stillfluctuating up and down at a certain central value but willgradually shrink with the magnitude of evolutionary fluc-tuations and the maximum peak of energy intensity is alsosignificantly smaller than before It also has a significantimpact on the evolution of environmental quality In thelong run the central value of the shock is decreasing theamplitude of the shock is decreasing and eventually it tendsto be stable After the pollution emission peak is loweredagain F 03816 the energy intensity and environmentalquality evolve to a stable value at a relatively fast rate and thepeak value of the energy intensity and the center value of theoscillation are reduced again before comparison -ereforeit can be better explained that effective control of the peakarrival time of pollution emissions can be used as an im-portant decision for pollution emission control and energyintensity reduction

From Figure 9(b) we can also find that the advance ofthe peak of pollution emissions makes the environmentalsystem take the risk ahead and the threat level is greatlyincreased -e reason for this phenomenon is that the peakof pollution discharge exceeds the self-purification speed ofthe natural environment system during the self-circulationprocess so that the accumulation of pollutants in the eco-logical environment system reaches the maximum capacityand the self-purification ability of the environmental system

is weakened In a relatively short period of time the eco-logical environment system is extremely deteriorated-erefore how to effectively and reasonably control the peakof pollution emission is very important for controlling thestability of 3E system and improving the environmentalquality

By comparing Figure 10(a) it can be found that in theshort term the environmental capacity of the ecosystem hasno significant effect on the stability of the evolution of the 3Esystem As the environmental capacity decreases over timethe evolution of environmental quality shows an upwardtrend of fluctuations and fluctuations around a certaincentral value when the capacity of the ecosystem falls to thelimit (ie the pollution effect exceeds the ecological envi-ronment) the system collapses (ie the ecological envi-ronment disappears and the ecosystem can no longer relyon self-regulation to repair the ecological environment) As aresult this situation continues and the ecological environ-ment is eventually sold out It is confirmed that the eco-logical environment system has a certain bearing capacityand the effect that the ecosystem will not be in operation orself-purification after the limit value can be exceeded is notsignificant

From Figure 10(b) we can find that the effect of simplyincreasing the economic investment in the environment toimprove the environmental quality is not obvious it doesnot increase the economic investment as expected and theenvironment can be effectively improved From the evolu-tionary trajectory of the system it can be seen that theevolutionary trajectory of the system revolves around centralvalue fluctuation and oscillation amplitude over time -isphenomenon shows that the effects of economic input in theprocess of environmental governance are not significantenough -erefore in order to improve the quality of theecological environment and promote the rapid developmentof the economy we need more measures to use more meansand technologies to promote stable economic growth andmanagement of the ecological environment It is necessaryto correctly grasp the ecological environment protection andthe relationship between economic developments explore

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash4

ndash3

ndash2

ndash1

0

1

2

Envi

ronm

enta

l qua

lity

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

(b)

Figure 8 -e parameters a3 on the influence of system (1)

Complexity 11

synergies to promote ecological priorities and green de-velopment new ideas and ultimately achieve a ldquowin-winrdquoenvironment and economy

5 Conclusion

In this study the energy economic and environmental (3E)four-dimensional system model of energy conservationconstraints was first established -e Bayesian estimationmethod is used to correct the environmental quality vari-ables to obtain the environmental quality data needed for theresearch In addition based on the Chinese statisticalyearbook data the LevenbergndashMarquardt BP neural net-work method optimized by genetic algorithm is used toenergy economy and environment under energy conser-vation constraints -e parameters in the four-dimensionalsystem model are effectively identified Finally the systemscience analysis theory and complex system dynamics theoryare used to analyze the stability and complex dynamics of the

model and explore the influence of some key parameters inthe four-dimensional system on the evolution stability of thesystem -e main conclusions are as follows

(1) Although increasing the investment in energy re-duction can effectively improve the environmentalquality in a relatively short period of time theimprovement of environmental quality is also veryobvious but in the long run the environment is stilldeteriorating with the decline in the discount rate ofenergy reduction inputs

(2) It can be better explained that effective control of thepeak arrival time of pollution emissions can be usedas an important decision for pollution emissioncontrol and energy intensity reduction thereforehow to effectively and reasonably control the peak ofpollution emissions is of great significance forcontrolling the stability of energy economy andenvironment system under the constraint of energy

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

(b)

Figure 9 -e parameters F on the influence of system (1)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redP = 05121 blue P = 06121 and green

P = 07121)

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redd3 = 02667 blue d3 = 03667 and green

d3 = 04667)

(b)

Figure 10 -e different parameters P and d3 on the influence of system (1)

12 Complexity

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

system (1) on initial conditions -e sensitivity of system(when losing stability) with (x y z w) (0015 0758

18315) (x1 y z w) (0014 0758 18315) and(x2 y z w) (0016 0758 18315) and a small change inthe initial conditions may cause a large change in the wholefour-dimensional system which indicates that the system issensitive to the initial state From Figure 5 we can also knowthat the initial values vary greatly in the trajectories of thedeviated system (1) Although the initial states are indistin-guishable the initial values will be quickly established afterseveral iterations which is also an important symbol ofchaotic motion

3 System Parameter Identification

31 Data Gathering On the basis of complex interactions afour-dimensional dynamic system that integrates restrictsand promotes energy conservation energy economy andenvironment is established In this study the determination ofthe parameters of the four-dimensional dynamic system is ofgreat significance to the actual research Because the envi-ronment energy intensity and economic growth are affectedby the changes of these variables based on the official statisticsand measured data of the China Statistical Yearbook geneticoptimization of the optimized LM-BP neural networkmethod

x

y

z

w

0

1

2

02 04 06 08 1 12 14 16 180 2t (103)

ndash10123

02 04 06 08 1 12 14 16 18 20t (103)

115

2

02 04 06 08 1 12 14 16 18 20t (103)

0

1

02 04 06 08 1 12 14 16 18 20t (103)

Figure 3 System (1) time sequences diagram

y

08

1

12

14

16

18

0008 001 0012 00140006c2

(a)

ndash012

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

Lyap

unov

expo

nent

s

0008 001 0012 00140006c2

(b)

Figure 4 With c2 isin [0006 0014] change system (1) (a) bifurcation diagram (b) Lyapunov exponential diagram of corresponding (a)

Complexity 7

is used to obtain the actual parameters of the four-dimen-sional system to further analyze the evolutionary relationshipbetween energy consumption energy economic growth andthe environment of the 3E system

In this paper we mainly use the calculation method ofenergy reduction that is now common in the world tocalculate the amount of skill emission reduction [18] -eprincipal component analysis method based on the co-variance matrix is used to calculate the environmentalquality index [1] to represent the data of the environmentalchange Data on energy consumption and economic growthare mainly derived from Chinarsquos official statistical yearbookIn addition in order to make the environmental qualityindex positive during the research process we also use thelogarithmic logic model for data standardization All thedata in Table 2 is a standardized process based on the 1999data -e final data is as follows

32 Model Validation -e LM-BP neural network methodoptimized by genetic algorithm has a good application in theparameter identification of nonlinear systems [1] and it hasgood identification accuracy which makes this methodwidely used in nonidentification of linear system parame-ters After system (1) is discretized the difference equation ofthe following form is obtained

x(k + 1) x(k) + T a1x(k)y

M minus 11113874 1113875 minus a2y + a3z + a4w1113876 1113877

y(k + 1) y(k) + T minus b1x + b2y1 minus y

F1113874 1113875 + b3z

1 minus z

E1113874 1113875 minus b4w1113876 1113877

z(k + 1) z(k) + T c1xx

N minus 11113874 1113875 minus c2y minus c3z minus c4w1113876 1113877

w(k + 1) w(k) + T d1x minus d2y + d3z1 minus z

H1113874 1113875 + d4w

y

P minus 11113874 11138751113876 1113877

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

In this study we used the former n minus 1 group of data asthe input data of the LM-BP neural network optimized bythe genetic algorithm and the post n minus 1 data as the outputdata of the LM-BP neural network optimized by the geneticalgorithm In addition the data needs to be normalized inxi (xi minus xmin)(xmax minus xmin) form All other parameterswill be set to random number and the identified errorcontrol 10minus 6 Finally the identified system parametersare asshown in Table 3

-e data of 1980 is selected as the initial value of system[000000085 0658 173 11211] and the true validity of theidentification parameters is further verified -e evolutiontrajectory of the system is shown in Figures 6 and 7 It can beseen from the phase diagram of the evolutionary trajectoryof the system that the evolution trajectory of the system ismulticycle and can always be in a stable mode -is explainsthe true effectiveness of the system from the side which isalso in line with the real situation

4 System Parameter Analysis

In order to fully understand the stability of the above four-dimensional system (1) as well as the changes and impacts ofenergy intensity how to effectively reduce energy intensitystabilize economic development improve the quality ofecological environment and seek for high-quality sus-tainable development models and strategies and suggestionsfor the coordinated development of energy economy andenvironment therefore it is necessary to conduct an in-depth analysis of some key parameters of the four-dimen-sional system (1)

In Figures 8(a) and 8(b) we can find that althoughincreasing the investment in energy saving and emissionreduction can effectively improve the environmental qualitythe effect on reducing energy intensity is not obvious Overtime the amplitudes of the evolutionary fluctuations ofenergy intensity and environmental quality oscillate around

0

02

04

06

08

1

12

14

16

Erro

r sta

rtin

g fro

m d

iffer

ent i

nitia

l con

ditio

ns

05 2 3 45351 415 25 50t (103)

x (x = 0016)x (x = 0015)x (x = 0014)

Figure 5 System (1) sensitivity analysis

Table 2 Statistics on energy reduction energy consumption GDPand environment in China

Year x y z w

2000 19626 10455 11085 098372001 36786 11066 12228 095952002 22791 12064 13482 093472003 12699 14020 15283 087472004 23033 16382 18062 077412005 19352 18594 20813 072422006 20778 20380 24509 064032007 39437 22156 30307 054552008 65583 22808 35976 047522009 32830 23912 38997 040612010 33307 25656 46020 036932011 36871 27534 54243 035652012 40130 28608 60326 032102013 39274 29659 66068 028172014 42167 30292 72151 025752015 42893 30583 76813 023222016 45925 31004 82872 021592017 46121 31942 92297 02147

8 Complexity

Tabl

e3

System

(1)identifi

estheactual

parameters

a1

a2

a3

a4

b1

b2

b3

b4

c 1c 2

c 3c 4

d1

d2

d3

d4

MF

EN

HP

01277

02338

01992

00115

01896

04325

03818

00141

07582

05265

05834

00534

00591

00191

02567

05892

06523

05816

06437

05573

06943

07121

Complexity 9

a certain value In a relatively short period of time theimprovement of environmental quality is also very obviousbut in the long run the environment is still deteriorating

with the decline in the discount rate of energy-saving andemission-reduction inputs -e oscillating amplitude ofenergy intensity will decrease significantly with the increase

2

1

008

0604

02ndash04

0y x

z

(a)

ndash040

x

w

z

1

05

0

ndash052

10

(b)

1

05

0

ndash05

w

z y

21

0 0204

0608

(c)

1

05

0

ndash05

w

0806

0402y ndash04

0x

(d)

Figure 6 -ree-dimensional spatial phase diagram of system (1) with identified parameters

08

06

04

02

y

xndash04ndash06 ndash02 0

(a)

2

1

0

z

xndash04 ndash02ndash06 0

(b)

w

xndash04 ndash02ndash06 0

1

0

ndash1

(c)

2

1

0

02 04 06 08

z

y

(d)

02 04 06 08y

w

1

0

ndash1

(e)

z

w

1

0

ndash10 1 2

(f )

Figure 7 Two-dimensional plane phase diagram of system (1) with identified parameters

10 Complexity

of energy-saving and emission-reduction input but there isno obvious effect on the peak energy intensity -erefore itis not obvious that the effect of reducing the energy intensityand improving the stability of environmental quality bysimply increasing the investment in energy saving andemission reduction is not obvious

From Figures 9(a) and 9(b) we can find that when thepeak value of pollution emissions F 05816 the evolutiontrajectories of energy intensity and environmental qualityshow fluctuations around a certain central value over time-is phenomenon will be very unfavorable to the im-provement of environmental quality in controlling pollutionemissions (ie the inability to effectively reflect the energyreduction policies) when F 04816 with the passage oftime energy intensity and environmental quality are stillfluctuating up and down at a certain central value but willgradually shrink with the magnitude of evolutionary fluc-tuations and the maximum peak of energy intensity is alsosignificantly smaller than before It also has a significantimpact on the evolution of environmental quality In thelong run the central value of the shock is decreasing theamplitude of the shock is decreasing and eventually it tendsto be stable After the pollution emission peak is loweredagain F 03816 the energy intensity and environmentalquality evolve to a stable value at a relatively fast rate and thepeak value of the energy intensity and the center value of theoscillation are reduced again before comparison -ereforeit can be better explained that effective control of the peakarrival time of pollution emissions can be used as an im-portant decision for pollution emission control and energyintensity reduction

From Figure 9(b) we can also find that the advance ofthe peak of pollution emissions makes the environmentalsystem take the risk ahead and the threat level is greatlyincreased -e reason for this phenomenon is that the peakof pollution discharge exceeds the self-purification speed ofthe natural environment system during the self-circulationprocess so that the accumulation of pollutants in the eco-logical environment system reaches the maximum capacityand the self-purification ability of the environmental system

is weakened In a relatively short period of time the eco-logical environment system is extremely deteriorated-erefore how to effectively and reasonably control the peakof pollution emission is very important for controlling thestability of 3E system and improving the environmentalquality

By comparing Figure 10(a) it can be found that in theshort term the environmental capacity of the ecosystem hasno significant effect on the stability of the evolution of the 3Esystem As the environmental capacity decreases over timethe evolution of environmental quality shows an upwardtrend of fluctuations and fluctuations around a certaincentral value when the capacity of the ecosystem falls to thelimit (ie the pollution effect exceeds the ecological envi-ronment) the system collapses (ie the ecological envi-ronment disappears and the ecosystem can no longer relyon self-regulation to repair the ecological environment) As aresult this situation continues and the ecological environ-ment is eventually sold out It is confirmed that the eco-logical environment system has a certain bearing capacityand the effect that the ecosystem will not be in operation orself-purification after the limit value can be exceeded is notsignificant

From Figure 10(b) we can find that the effect of simplyincreasing the economic investment in the environment toimprove the environmental quality is not obvious it doesnot increase the economic investment as expected and theenvironment can be effectively improved From the evolu-tionary trajectory of the system it can be seen that theevolutionary trajectory of the system revolves around centralvalue fluctuation and oscillation amplitude over time -isphenomenon shows that the effects of economic input in theprocess of environmental governance are not significantenough -erefore in order to improve the quality of theecological environment and promote the rapid developmentof the economy we need more measures to use more meansand technologies to promote stable economic growth andmanagement of the ecological environment It is necessaryto correctly grasp the ecological environment protection andthe relationship between economic developments explore

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash4

ndash3

ndash2

ndash1

0

1

2

Envi

ronm

enta

l qua

lity

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

(b)

Figure 8 -e parameters a3 on the influence of system (1)

Complexity 11

synergies to promote ecological priorities and green de-velopment new ideas and ultimately achieve a ldquowin-winrdquoenvironment and economy

5 Conclusion

In this study the energy economic and environmental (3E)four-dimensional system model of energy conservationconstraints was first established -e Bayesian estimationmethod is used to correct the environmental quality vari-ables to obtain the environmental quality data needed for theresearch In addition based on the Chinese statisticalyearbook data the LevenbergndashMarquardt BP neural net-work method optimized by genetic algorithm is used toenergy economy and environment under energy conser-vation constraints -e parameters in the four-dimensionalsystem model are effectively identified Finally the systemscience analysis theory and complex system dynamics theoryare used to analyze the stability and complex dynamics of the

model and explore the influence of some key parameters inthe four-dimensional system on the evolution stability of thesystem -e main conclusions are as follows

(1) Although increasing the investment in energy re-duction can effectively improve the environmentalquality in a relatively short period of time theimprovement of environmental quality is also veryobvious but in the long run the environment is stilldeteriorating with the decline in the discount rate ofenergy reduction inputs

(2) It can be better explained that effective control of thepeak arrival time of pollution emissions can be usedas an important decision for pollution emissioncontrol and energy intensity reduction thereforehow to effectively and reasonably control the peak ofpollution emissions is of great significance forcontrolling the stability of energy economy andenvironment system under the constraint of energy

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

(b)

Figure 9 -e parameters F on the influence of system (1)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redP = 05121 blue P = 06121 and green

P = 07121)

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redd3 = 02667 blue d3 = 03667 and green

d3 = 04667)

(b)

Figure 10 -e different parameters P and d3 on the influence of system (1)

12 Complexity

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

is used to obtain the actual parameters of the four-dimen-sional system to further analyze the evolutionary relationshipbetween energy consumption energy economic growth andthe environment of the 3E system

In this paper we mainly use the calculation method ofenergy reduction that is now common in the world tocalculate the amount of skill emission reduction [18] -eprincipal component analysis method based on the co-variance matrix is used to calculate the environmentalquality index [1] to represent the data of the environmentalchange Data on energy consumption and economic growthare mainly derived from Chinarsquos official statistical yearbookIn addition in order to make the environmental qualityindex positive during the research process we also use thelogarithmic logic model for data standardization All thedata in Table 2 is a standardized process based on the 1999data -e final data is as follows

32 Model Validation -e LM-BP neural network methodoptimized by genetic algorithm has a good application in theparameter identification of nonlinear systems [1] and it hasgood identification accuracy which makes this methodwidely used in nonidentification of linear system parame-ters After system (1) is discretized the difference equation ofthe following form is obtained

x(k + 1) x(k) + T a1x(k)y

M minus 11113874 1113875 minus a2y + a3z + a4w1113876 1113877

y(k + 1) y(k) + T minus b1x + b2y1 minus y

F1113874 1113875 + b3z

1 minus z

E1113874 1113875 minus b4w1113876 1113877

z(k + 1) z(k) + T c1xx

N minus 11113874 1113875 minus c2y minus c3z minus c4w1113876 1113877

w(k + 1) w(k) + T d1x minus d2y + d3z1 minus z

H1113874 1113875 + d4w

y

P minus 11113874 11138751113876 1113877

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

In this study we used the former n minus 1 group of data asthe input data of the LM-BP neural network optimized bythe genetic algorithm and the post n minus 1 data as the outputdata of the LM-BP neural network optimized by the geneticalgorithm In addition the data needs to be normalized inxi (xi minus xmin)(xmax minus xmin) form All other parameterswill be set to random number and the identified errorcontrol 10minus 6 Finally the identified system parametersare asshown in Table 3

-e data of 1980 is selected as the initial value of system[000000085 0658 173 11211] and the true validity of theidentification parameters is further verified -e evolutiontrajectory of the system is shown in Figures 6 and 7 It can beseen from the phase diagram of the evolutionary trajectoryof the system that the evolution trajectory of the system ismulticycle and can always be in a stable mode -is explainsthe true effectiveness of the system from the side which isalso in line with the real situation

4 System Parameter Analysis

In order to fully understand the stability of the above four-dimensional system (1) as well as the changes and impacts ofenergy intensity how to effectively reduce energy intensitystabilize economic development improve the quality ofecological environment and seek for high-quality sus-tainable development models and strategies and suggestionsfor the coordinated development of energy economy andenvironment therefore it is necessary to conduct an in-depth analysis of some key parameters of the four-dimen-sional system (1)

In Figures 8(a) and 8(b) we can find that althoughincreasing the investment in energy saving and emissionreduction can effectively improve the environmental qualitythe effect on reducing energy intensity is not obvious Overtime the amplitudes of the evolutionary fluctuations ofenergy intensity and environmental quality oscillate around

0

02

04

06

08

1

12

14

16

Erro

r sta

rtin

g fro

m d

iffer

ent i

nitia

l con

ditio

ns

05 2 3 45351 415 25 50t (103)

x (x = 0016)x (x = 0015)x (x = 0014)

Figure 5 System (1) sensitivity analysis

Table 2 Statistics on energy reduction energy consumption GDPand environment in China

Year x y z w

2000 19626 10455 11085 098372001 36786 11066 12228 095952002 22791 12064 13482 093472003 12699 14020 15283 087472004 23033 16382 18062 077412005 19352 18594 20813 072422006 20778 20380 24509 064032007 39437 22156 30307 054552008 65583 22808 35976 047522009 32830 23912 38997 040612010 33307 25656 46020 036932011 36871 27534 54243 035652012 40130 28608 60326 032102013 39274 29659 66068 028172014 42167 30292 72151 025752015 42893 30583 76813 023222016 45925 31004 82872 021592017 46121 31942 92297 02147

8 Complexity

Tabl

e3

System

(1)identifi

estheactual

parameters

a1

a2

a3

a4

b1

b2

b3

b4

c 1c 2

c 3c 4

d1

d2

d3

d4

MF

EN

HP

01277

02338

01992

00115

01896

04325

03818

00141

07582

05265

05834

00534

00591

00191

02567

05892

06523

05816

06437

05573

06943

07121

Complexity 9

a certain value In a relatively short period of time theimprovement of environmental quality is also very obviousbut in the long run the environment is still deteriorating

with the decline in the discount rate of energy-saving andemission-reduction inputs -e oscillating amplitude ofenergy intensity will decrease significantly with the increase

2

1

008

0604

02ndash04

0y x

z

(a)

ndash040

x

w

z

1

05

0

ndash052

10

(b)

1

05

0

ndash05

w

z y

21

0 0204

0608

(c)

1

05

0

ndash05

w

0806

0402y ndash04

0x

(d)

Figure 6 -ree-dimensional spatial phase diagram of system (1) with identified parameters

08

06

04

02

y

xndash04ndash06 ndash02 0

(a)

2

1

0

z

xndash04 ndash02ndash06 0

(b)

w

xndash04 ndash02ndash06 0

1

0

ndash1

(c)

2

1

0

02 04 06 08

z

y

(d)

02 04 06 08y

w

1

0

ndash1

(e)

z

w

1

0

ndash10 1 2

(f )

Figure 7 Two-dimensional plane phase diagram of system (1) with identified parameters

10 Complexity

of energy-saving and emission-reduction input but there isno obvious effect on the peak energy intensity -erefore itis not obvious that the effect of reducing the energy intensityand improving the stability of environmental quality bysimply increasing the investment in energy saving andemission reduction is not obvious

From Figures 9(a) and 9(b) we can find that when thepeak value of pollution emissions F 05816 the evolutiontrajectories of energy intensity and environmental qualityshow fluctuations around a certain central value over time-is phenomenon will be very unfavorable to the im-provement of environmental quality in controlling pollutionemissions (ie the inability to effectively reflect the energyreduction policies) when F 04816 with the passage oftime energy intensity and environmental quality are stillfluctuating up and down at a certain central value but willgradually shrink with the magnitude of evolutionary fluc-tuations and the maximum peak of energy intensity is alsosignificantly smaller than before It also has a significantimpact on the evolution of environmental quality In thelong run the central value of the shock is decreasing theamplitude of the shock is decreasing and eventually it tendsto be stable After the pollution emission peak is loweredagain F 03816 the energy intensity and environmentalquality evolve to a stable value at a relatively fast rate and thepeak value of the energy intensity and the center value of theoscillation are reduced again before comparison -ereforeit can be better explained that effective control of the peakarrival time of pollution emissions can be used as an im-portant decision for pollution emission control and energyintensity reduction

From Figure 9(b) we can also find that the advance ofthe peak of pollution emissions makes the environmentalsystem take the risk ahead and the threat level is greatlyincreased -e reason for this phenomenon is that the peakof pollution discharge exceeds the self-purification speed ofthe natural environment system during the self-circulationprocess so that the accumulation of pollutants in the eco-logical environment system reaches the maximum capacityand the self-purification ability of the environmental system

is weakened In a relatively short period of time the eco-logical environment system is extremely deteriorated-erefore how to effectively and reasonably control the peakof pollution emission is very important for controlling thestability of 3E system and improving the environmentalquality

By comparing Figure 10(a) it can be found that in theshort term the environmental capacity of the ecosystem hasno significant effect on the stability of the evolution of the 3Esystem As the environmental capacity decreases over timethe evolution of environmental quality shows an upwardtrend of fluctuations and fluctuations around a certaincentral value when the capacity of the ecosystem falls to thelimit (ie the pollution effect exceeds the ecological envi-ronment) the system collapses (ie the ecological envi-ronment disappears and the ecosystem can no longer relyon self-regulation to repair the ecological environment) As aresult this situation continues and the ecological environ-ment is eventually sold out It is confirmed that the eco-logical environment system has a certain bearing capacityand the effect that the ecosystem will not be in operation orself-purification after the limit value can be exceeded is notsignificant

From Figure 10(b) we can find that the effect of simplyincreasing the economic investment in the environment toimprove the environmental quality is not obvious it doesnot increase the economic investment as expected and theenvironment can be effectively improved From the evolu-tionary trajectory of the system it can be seen that theevolutionary trajectory of the system revolves around centralvalue fluctuation and oscillation amplitude over time -isphenomenon shows that the effects of economic input in theprocess of environmental governance are not significantenough -erefore in order to improve the quality of theecological environment and promote the rapid developmentof the economy we need more measures to use more meansand technologies to promote stable economic growth andmanagement of the ecological environment It is necessaryto correctly grasp the ecological environment protection andthe relationship between economic developments explore

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash4

ndash3

ndash2

ndash1

0

1

2

Envi

ronm

enta

l qua

lity

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

(b)

Figure 8 -e parameters a3 on the influence of system (1)

Complexity 11

synergies to promote ecological priorities and green de-velopment new ideas and ultimately achieve a ldquowin-winrdquoenvironment and economy

5 Conclusion

In this study the energy economic and environmental (3E)four-dimensional system model of energy conservationconstraints was first established -e Bayesian estimationmethod is used to correct the environmental quality vari-ables to obtain the environmental quality data needed for theresearch In addition based on the Chinese statisticalyearbook data the LevenbergndashMarquardt BP neural net-work method optimized by genetic algorithm is used toenergy economy and environment under energy conser-vation constraints -e parameters in the four-dimensionalsystem model are effectively identified Finally the systemscience analysis theory and complex system dynamics theoryare used to analyze the stability and complex dynamics of the

model and explore the influence of some key parameters inthe four-dimensional system on the evolution stability of thesystem -e main conclusions are as follows

(1) Although increasing the investment in energy re-duction can effectively improve the environmentalquality in a relatively short period of time theimprovement of environmental quality is also veryobvious but in the long run the environment is stilldeteriorating with the decline in the discount rate ofenergy reduction inputs

(2) It can be better explained that effective control of thepeak arrival time of pollution emissions can be usedas an important decision for pollution emissioncontrol and energy intensity reduction thereforehow to effectively and reasonably control the peak ofpollution emissions is of great significance forcontrolling the stability of energy economy andenvironment system under the constraint of energy

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

(b)

Figure 9 -e parameters F on the influence of system (1)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redP = 05121 blue P = 06121 and green

P = 07121)

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redd3 = 02667 blue d3 = 03667 and green

d3 = 04667)

(b)

Figure 10 -e different parameters P and d3 on the influence of system (1)

12 Complexity

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

Tabl

e3

System

(1)identifi

estheactual

parameters

a1

a2

a3

a4

b1

b2

b3

b4

c 1c 2

c 3c 4

d1

d2

d3

d4

MF

EN

HP

01277

02338

01992

00115

01896

04325

03818

00141

07582

05265

05834

00534

00591

00191

02567

05892

06523

05816

06437

05573

06943

07121

Complexity 9

a certain value In a relatively short period of time theimprovement of environmental quality is also very obviousbut in the long run the environment is still deteriorating

with the decline in the discount rate of energy-saving andemission-reduction inputs -e oscillating amplitude ofenergy intensity will decrease significantly with the increase

2

1

008

0604

02ndash04

0y x

z

(a)

ndash040

x

w

z

1

05

0

ndash052

10

(b)

1

05

0

ndash05

w

z y

21

0 0204

0608

(c)

1

05

0

ndash05

w

0806

0402y ndash04

0x

(d)

Figure 6 -ree-dimensional spatial phase diagram of system (1) with identified parameters

08

06

04

02

y

xndash04ndash06 ndash02 0

(a)

2

1

0

z

xndash04 ndash02ndash06 0

(b)

w

xndash04 ndash02ndash06 0

1

0

ndash1

(c)

2

1

0

02 04 06 08

z

y

(d)

02 04 06 08y

w

1

0

ndash1

(e)

z

w

1

0

ndash10 1 2

(f )

Figure 7 Two-dimensional plane phase diagram of system (1) with identified parameters

10 Complexity

of energy-saving and emission-reduction input but there isno obvious effect on the peak energy intensity -erefore itis not obvious that the effect of reducing the energy intensityand improving the stability of environmental quality bysimply increasing the investment in energy saving andemission reduction is not obvious

From Figures 9(a) and 9(b) we can find that when thepeak value of pollution emissions F 05816 the evolutiontrajectories of energy intensity and environmental qualityshow fluctuations around a certain central value over time-is phenomenon will be very unfavorable to the im-provement of environmental quality in controlling pollutionemissions (ie the inability to effectively reflect the energyreduction policies) when F 04816 with the passage oftime energy intensity and environmental quality are stillfluctuating up and down at a certain central value but willgradually shrink with the magnitude of evolutionary fluc-tuations and the maximum peak of energy intensity is alsosignificantly smaller than before It also has a significantimpact on the evolution of environmental quality In thelong run the central value of the shock is decreasing theamplitude of the shock is decreasing and eventually it tendsto be stable After the pollution emission peak is loweredagain F 03816 the energy intensity and environmentalquality evolve to a stable value at a relatively fast rate and thepeak value of the energy intensity and the center value of theoscillation are reduced again before comparison -ereforeit can be better explained that effective control of the peakarrival time of pollution emissions can be used as an im-portant decision for pollution emission control and energyintensity reduction

From Figure 9(b) we can also find that the advance ofthe peak of pollution emissions makes the environmentalsystem take the risk ahead and the threat level is greatlyincreased -e reason for this phenomenon is that the peakof pollution discharge exceeds the self-purification speed ofthe natural environment system during the self-circulationprocess so that the accumulation of pollutants in the eco-logical environment system reaches the maximum capacityand the self-purification ability of the environmental system

is weakened In a relatively short period of time the eco-logical environment system is extremely deteriorated-erefore how to effectively and reasonably control the peakof pollution emission is very important for controlling thestability of 3E system and improving the environmentalquality

By comparing Figure 10(a) it can be found that in theshort term the environmental capacity of the ecosystem hasno significant effect on the stability of the evolution of the 3Esystem As the environmental capacity decreases over timethe evolution of environmental quality shows an upwardtrend of fluctuations and fluctuations around a certaincentral value when the capacity of the ecosystem falls to thelimit (ie the pollution effect exceeds the ecological envi-ronment) the system collapses (ie the ecological envi-ronment disappears and the ecosystem can no longer relyon self-regulation to repair the ecological environment) As aresult this situation continues and the ecological environ-ment is eventually sold out It is confirmed that the eco-logical environment system has a certain bearing capacityand the effect that the ecosystem will not be in operation orself-purification after the limit value can be exceeded is notsignificant

From Figure 10(b) we can find that the effect of simplyincreasing the economic investment in the environment toimprove the environmental quality is not obvious it doesnot increase the economic investment as expected and theenvironment can be effectively improved From the evolu-tionary trajectory of the system it can be seen that theevolutionary trajectory of the system revolves around centralvalue fluctuation and oscillation amplitude over time -isphenomenon shows that the effects of economic input in theprocess of environmental governance are not significantenough -erefore in order to improve the quality of theecological environment and promote the rapid developmentof the economy we need more measures to use more meansand technologies to promote stable economic growth andmanagement of the ecological environment It is necessaryto correctly grasp the ecological environment protection andthe relationship between economic developments explore

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash4

ndash3

ndash2

ndash1

0

1

2

Envi

ronm

enta

l qua

lity

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

(b)

Figure 8 -e parameters a3 on the influence of system (1)

Complexity 11

synergies to promote ecological priorities and green de-velopment new ideas and ultimately achieve a ldquowin-winrdquoenvironment and economy

5 Conclusion

In this study the energy economic and environmental (3E)four-dimensional system model of energy conservationconstraints was first established -e Bayesian estimationmethod is used to correct the environmental quality vari-ables to obtain the environmental quality data needed for theresearch In addition based on the Chinese statisticalyearbook data the LevenbergndashMarquardt BP neural net-work method optimized by genetic algorithm is used toenergy economy and environment under energy conser-vation constraints -e parameters in the four-dimensionalsystem model are effectively identified Finally the systemscience analysis theory and complex system dynamics theoryare used to analyze the stability and complex dynamics of the

model and explore the influence of some key parameters inthe four-dimensional system on the evolution stability of thesystem -e main conclusions are as follows

(1) Although increasing the investment in energy re-duction can effectively improve the environmentalquality in a relatively short period of time theimprovement of environmental quality is also veryobvious but in the long run the environment is stilldeteriorating with the decline in the discount rate ofenergy reduction inputs

(2) It can be better explained that effective control of thepeak arrival time of pollution emissions can be usedas an important decision for pollution emissioncontrol and energy intensity reduction thereforehow to effectively and reasonably control the peak ofpollution emissions is of great significance forcontrolling the stability of energy economy andenvironment system under the constraint of energy

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

(b)

Figure 9 -e parameters F on the influence of system (1)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redP = 05121 blue P = 06121 and green

P = 07121)

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redd3 = 02667 blue d3 = 03667 and green

d3 = 04667)

(b)

Figure 10 -e different parameters P and d3 on the influence of system (1)

12 Complexity

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

a certain value In a relatively short period of time theimprovement of environmental quality is also very obviousbut in the long run the environment is still deteriorating

with the decline in the discount rate of energy-saving andemission-reduction inputs -e oscillating amplitude ofenergy intensity will decrease significantly with the increase

2

1

008

0604

02ndash04

0y x

z

(a)

ndash040

x

w

z

1

05

0

ndash052

10

(b)

1

05

0

ndash05

w

z y

21

0 0204

0608

(c)

1

05

0

ndash05

w

0806

0402y ndash04

0x

(d)

Figure 6 -ree-dimensional spatial phase diagram of system (1) with identified parameters

08

06

04

02

y

xndash04ndash06 ndash02 0

(a)

2

1

0

z

xndash04 ndash02ndash06 0

(b)

w

xndash04 ndash02ndash06 0

1

0

ndash1

(c)

2

1

0

02 04 06 08

z

y

(d)

02 04 06 08y

w

1

0

ndash1

(e)

z

w

1

0

ndash10 1 2

(f )

Figure 7 Two-dimensional plane phase diagram of system (1) with identified parameters

10 Complexity

of energy-saving and emission-reduction input but there isno obvious effect on the peak energy intensity -erefore itis not obvious that the effect of reducing the energy intensityand improving the stability of environmental quality bysimply increasing the investment in energy saving andemission reduction is not obvious

From Figures 9(a) and 9(b) we can find that when thepeak value of pollution emissions F 05816 the evolutiontrajectories of energy intensity and environmental qualityshow fluctuations around a certain central value over time-is phenomenon will be very unfavorable to the im-provement of environmental quality in controlling pollutionemissions (ie the inability to effectively reflect the energyreduction policies) when F 04816 with the passage oftime energy intensity and environmental quality are stillfluctuating up and down at a certain central value but willgradually shrink with the magnitude of evolutionary fluc-tuations and the maximum peak of energy intensity is alsosignificantly smaller than before It also has a significantimpact on the evolution of environmental quality In thelong run the central value of the shock is decreasing theamplitude of the shock is decreasing and eventually it tendsto be stable After the pollution emission peak is loweredagain F 03816 the energy intensity and environmentalquality evolve to a stable value at a relatively fast rate and thepeak value of the energy intensity and the center value of theoscillation are reduced again before comparison -ereforeit can be better explained that effective control of the peakarrival time of pollution emissions can be used as an im-portant decision for pollution emission control and energyintensity reduction

From Figure 9(b) we can also find that the advance ofthe peak of pollution emissions makes the environmentalsystem take the risk ahead and the threat level is greatlyincreased -e reason for this phenomenon is that the peakof pollution discharge exceeds the self-purification speed ofthe natural environment system during the self-circulationprocess so that the accumulation of pollutants in the eco-logical environment system reaches the maximum capacityand the self-purification ability of the environmental system

is weakened In a relatively short period of time the eco-logical environment system is extremely deteriorated-erefore how to effectively and reasonably control the peakof pollution emission is very important for controlling thestability of 3E system and improving the environmentalquality

By comparing Figure 10(a) it can be found that in theshort term the environmental capacity of the ecosystem hasno significant effect on the stability of the evolution of the 3Esystem As the environmental capacity decreases over timethe evolution of environmental quality shows an upwardtrend of fluctuations and fluctuations around a certaincentral value when the capacity of the ecosystem falls to thelimit (ie the pollution effect exceeds the ecological envi-ronment) the system collapses (ie the ecological envi-ronment disappears and the ecosystem can no longer relyon self-regulation to repair the ecological environment) As aresult this situation continues and the ecological environ-ment is eventually sold out It is confirmed that the eco-logical environment system has a certain bearing capacityand the effect that the ecosystem will not be in operation orself-purification after the limit value can be exceeded is notsignificant

From Figure 10(b) we can find that the effect of simplyincreasing the economic investment in the environment toimprove the environmental quality is not obvious it doesnot increase the economic investment as expected and theenvironment can be effectively improved From the evolu-tionary trajectory of the system it can be seen that theevolutionary trajectory of the system revolves around centralvalue fluctuation and oscillation amplitude over time -isphenomenon shows that the effects of economic input in theprocess of environmental governance are not significantenough -erefore in order to improve the quality of theecological environment and promote the rapid developmentof the economy we need more measures to use more meansand technologies to promote stable economic growth andmanagement of the ecological environment It is necessaryto correctly grasp the ecological environment protection andthe relationship between economic developments explore

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash4

ndash3

ndash2

ndash1

0

1

2

Envi

ronm

enta

l qua

lity

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

(b)

Figure 8 -e parameters a3 on the influence of system (1)

Complexity 11

synergies to promote ecological priorities and green de-velopment new ideas and ultimately achieve a ldquowin-winrdquoenvironment and economy

5 Conclusion

In this study the energy economic and environmental (3E)four-dimensional system model of energy conservationconstraints was first established -e Bayesian estimationmethod is used to correct the environmental quality vari-ables to obtain the environmental quality data needed for theresearch In addition based on the Chinese statisticalyearbook data the LevenbergndashMarquardt BP neural net-work method optimized by genetic algorithm is used toenergy economy and environment under energy conser-vation constraints -e parameters in the four-dimensionalsystem model are effectively identified Finally the systemscience analysis theory and complex system dynamics theoryare used to analyze the stability and complex dynamics of the

model and explore the influence of some key parameters inthe four-dimensional system on the evolution stability of thesystem -e main conclusions are as follows

(1) Although increasing the investment in energy re-duction can effectively improve the environmentalquality in a relatively short period of time theimprovement of environmental quality is also veryobvious but in the long run the environment is stilldeteriorating with the decline in the discount rate ofenergy reduction inputs

(2) It can be better explained that effective control of thepeak arrival time of pollution emissions can be usedas an important decision for pollution emissioncontrol and energy intensity reduction thereforehow to effectively and reasonably control the peak ofpollution emissions is of great significance forcontrolling the stability of energy economy andenvironment system under the constraint of energy

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

(b)

Figure 9 -e parameters F on the influence of system (1)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redP = 05121 blue P = 06121 and green

P = 07121)

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redd3 = 02667 blue d3 = 03667 and green

d3 = 04667)

(b)

Figure 10 -e different parameters P and d3 on the influence of system (1)

12 Complexity

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

of energy-saving and emission-reduction input but there isno obvious effect on the peak energy intensity -erefore itis not obvious that the effect of reducing the energy intensityand improving the stability of environmental quality bysimply increasing the investment in energy saving andemission reduction is not obvious

From Figures 9(a) and 9(b) we can find that when thepeak value of pollution emissions F 05816 the evolutiontrajectories of energy intensity and environmental qualityshow fluctuations around a certain central value over time-is phenomenon will be very unfavorable to the im-provement of environmental quality in controlling pollutionemissions (ie the inability to effectively reflect the energyreduction policies) when F 04816 with the passage oftime energy intensity and environmental quality are stillfluctuating up and down at a certain central value but willgradually shrink with the magnitude of evolutionary fluc-tuations and the maximum peak of energy intensity is alsosignificantly smaller than before It also has a significantimpact on the evolution of environmental quality In thelong run the central value of the shock is decreasing theamplitude of the shock is decreasing and eventually it tendsto be stable After the pollution emission peak is loweredagain F 03816 the energy intensity and environmentalquality evolve to a stable value at a relatively fast rate and thepeak value of the energy intensity and the center value of theoscillation are reduced again before comparison -ereforeit can be better explained that effective control of the peakarrival time of pollution emissions can be used as an im-portant decision for pollution emission control and energyintensity reduction

From Figure 9(b) we can also find that the advance ofthe peak of pollution emissions makes the environmentalsystem take the risk ahead and the threat level is greatlyincreased -e reason for this phenomenon is that the peakof pollution discharge exceeds the self-purification speed ofthe natural environment system during the self-circulationprocess so that the accumulation of pollutants in the eco-logical environment system reaches the maximum capacityand the self-purification ability of the environmental system

is weakened In a relatively short period of time the eco-logical environment system is extremely deteriorated-erefore how to effectively and reasonably control the peakof pollution emission is very important for controlling thestability of 3E system and improving the environmentalquality

By comparing Figure 10(a) it can be found that in theshort term the environmental capacity of the ecosystem hasno significant effect on the stability of the evolution of the 3Esystem As the environmental capacity decreases over timethe evolution of environmental quality shows an upwardtrend of fluctuations and fluctuations around a certaincentral value when the capacity of the ecosystem falls to thelimit (ie the pollution effect exceeds the ecological envi-ronment) the system collapses (ie the ecological envi-ronment disappears and the ecosystem can no longer relyon self-regulation to repair the ecological environment) As aresult this situation continues and the ecological environ-ment is eventually sold out It is confirmed that the eco-logical environment system has a certain bearing capacityand the effect that the ecosystem will not be in operation orself-purification after the limit value can be exceeded is notsignificant

From Figure 10(b) we can find that the effect of simplyincreasing the economic investment in the environment toimprove the environmental quality is not obvious it doesnot increase the economic investment as expected and theenvironment can be effectively improved From the evolu-tionary trajectory of the system it can be seen that theevolutionary trajectory of the system revolves around centralvalue fluctuation and oscillation amplitude over time -isphenomenon shows that the effects of economic input in theprocess of environmental governance are not significantenough -erefore in order to improve the quality of theecological environment and promote the rapid developmentof the economy we need more measures to use more meansand technologies to promote stable economic growth andmanagement of the ecological environment It is necessaryto correctly grasp the ecological environment protection andthe relationship between economic developments explore

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash4

ndash3

ndash2

ndash1

0

1

2

Envi

ronm

enta

l qua

lity

4020 3010 500t (reda3 = 01992 blue a3 = 02192 and green

a3 = 02592)

(b)

Figure 8 -e parameters a3 on the influence of system (1)

Complexity 11

synergies to promote ecological priorities and green de-velopment new ideas and ultimately achieve a ldquowin-winrdquoenvironment and economy

5 Conclusion

In this study the energy economic and environmental (3E)four-dimensional system model of energy conservationconstraints was first established -e Bayesian estimationmethod is used to correct the environmental quality vari-ables to obtain the environmental quality data needed for theresearch In addition based on the Chinese statisticalyearbook data the LevenbergndashMarquardt BP neural net-work method optimized by genetic algorithm is used toenergy economy and environment under energy conser-vation constraints -e parameters in the four-dimensionalsystem model are effectively identified Finally the systemscience analysis theory and complex system dynamics theoryare used to analyze the stability and complex dynamics of the

model and explore the influence of some key parameters inthe four-dimensional system on the evolution stability of thesystem -e main conclusions are as follows

(1) Although increasing the investment in energy re-duction can effectively improve the environmentalquality in a relatively short period of time theimprovement of environmental quality is also veryobvious but in the long run the environment is stilldeteriorating with the decline in the discount rate ofenergy reduction inputs

(2) It can be better explained that effective control of thepeak arrival time of pollution emissions can be usedas an important decision for pollution emissioncontrol and energy intensity reduction thereforehow to effectively and reasonably control the peak ofpollution emissions is of great significance forcontrolling the stability of energy economy andenvironment system under the constraint of energy

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

(b)

Figure 9 -e parameters F on the influence of system (1)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redP = 05121 blue P = 06121 and green

P = 07121)

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redd3 = 02667 blue d3 = 03667 and green

d3 = 04667)

(b)

Figure 10 -e different parameters P and d3 on the influence of system (1)

12 Complexity

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

synergies to promote ecological priorities and green de-velopment new ideas and ultimately achieve a ldquowin-winrdquoenvironment and economy

5 Conclusion

In this study the energy economic and environmental (3E)four-dimensional system model of energy conservationconstraints was first established -e Bayesian estimationmethod is used to correct the environmental quality vari-ables to obtain the environmental quality data needed for theresearch In addition based on the Chinese statisticalyearbook data the LevenbergndashMarquardt BP neural net-work method optimized by genetic algorithm is used toenergy economy and environment under energy conser-vation constraints -e parameters in the four-dimensionalsystem model are effectively identified Finally the systemscience analysis theory and complex system dynamics theoryare used to analyze the stability and complex dynamics of the

model and explore the influence of some key parameters inthe four-dimensional system on the evolution stability of thesystem -e main conclusions are as follows

(1) Although increasing the investment in energy re-duction can effectively improve the environmentalquality in a relatively short period of time theimprovement of environmental quality is also veryobvious but in the long run the environment is stilldeteriorating with the decline in the discount rate ofenergy reduction inputs

(2) It can be better explained that effective control of thepeak arrival time of pollution emissions can be usedas an important decision for pollution emissioncontrol and energy intensity reduction thereforehow to effectively and reasonably control the peak ofpollution emissions is of great significance forcontrolling the stability of energy economy andenvironment system under the constraint of energy

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

05

04

03

02

01

0

Ener

gy in

tens

ity

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redF = 05816 blue F = 04816 and green

F = 03816)

(b)

Figure 9 -e parameters F on the influence of system (1)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redP = 05121 blue P = 06121 and green

P = 07121)

(a)

ndash1

ndash05

0

05

1

15

Envi

ronm

enta

l qua

lity

10 20 30 40 500t (redd3 = 02667 blue d3 = 03667 and green

d3 = 04667)

(b)

Figure 10 -e different parameters P and d3 on the influence of system (1)

12 Complexity

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

reduction regulating energy intensity and im-proving environmental quality and sustainabledevelopment

(3) As the environmental capacity decreases over timethe evolution of environmental quality shows anupward trend of fluctuations and fluctuationsaround a certain central value when the capacity ofthe ecosystem falls to the limit the system collapsesIn order to improve the quality of the ecologicalenvironment and promote the rapid development ofthe economy we need more measures to use moremeans and technologies to promote stable economicgrowth and management of the ecologicalenvironment

-erefore it is necessary to correctly grasp the ecologicalenvironment protection and the relationship between eco-nomic developments and explore synergies to promoteecological priorities and green development new ideas

Data Availability

-e numerical simulations data used to support the findingsof this study were supplied by the corresponding authorunder license and so cannot be made freely available Re-quests for access to these data should be made to the cor-responding author (e-mail address 136901672qqcom)

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Nature ScienceFoundation of China (no 71974081) Humanities and SocialSciences Research Project of the Ministry of Education ofChina (17YJAZH035) the Philosophy and Social ScienceFund for University of Jiangsu (no 2019SJA1051) andJiangsu University of Technology Talent IntroductionProject (KYY18539)

References

[1] L Zhao C Otoo and A Otoo ldquoStability and complexity of anovel three-dimensional environmental quality dynamicevolution systemrdquo Complexity vol 2019 Article ID 394192011 pages 2019

[2] G Fang L Tian M Sun andM Fu ldquoAnalysis and applicationof a novel three-dimensional energy-saving and emission-reduction dynamic evolution systemrdquo Energy vol 40 no 1pp 291ndash299 2012

[3] R K Upadhyay S R K Iyengar and V Rai ldquoStability andcomplexity in ecological systemsrdquo Chaos Solitons amp Fractalsvol 11 no 4 pp 533ndash542 2000

[4] J Asafu-Adjaye ldquo-e relationship between energy con-sumption energy prices and economic growth time seriesevidence from Asian developing countriesrdquo Energy Eco-nomics vol 22 no 6 pp 615ndash625 2000

[5] G Hondroyiannis S Lolos and E Papapetrou ldquoEnergyconsumption and economic growth assessing the evidence

from Greecerdquo Energy Economics vol 24 no 4 pp 319ndash3362002

[6] S Wang J Xu and C Qiu ldquoBounds testing for energyconsumption and environmental pollutionrdquo China Pop-ulation Resources and Environment vol 20 no 4 pp 69ndash732010

[7] L I Guozhang J Jiang and C Zhou ldquoRelation between totalfactor energy efficiency and environmental pollutionrdquo ChinaPopulation Resources and Environment vol 20 no 4pp 50ndash56 2010

[8] R Lopez ldquo-e environment as a factor of production theeffects of economic growth and trade liberalizationrdquo Journalof Environmental Economics and Management vol 27 no 2pp 163ndash184 1994

[9] A Grainger ldquo-e forest transition an alternative approachrdquoArea vol 3 pp 242ndash251 1998

[10] M Shahbaz N Khraief G S Uddin and I Ozturk ldquoEnvi-ronmental Kuznets curve in an open economy a boundstesting and causality analysis for Tunisiardquo Renewable ampSustainable Energy Reviews vol 34 pp 325ndash336 2014

[11] J Andreoni and A Levinson ldquo-e simple analytics of theenvironmental Kuznets curverdquo Journal of Public Economicsvol 80 no 2 pp 269ndash286 2001

[12] E Magnani ldquo-e Environmental Kuznets Curve develop-ment path or policy resultrdquo Environmental Modelling ampSoftware vol 16 no 2 pp 157ndash165 2001

[13] A K Bello and O M Abimbola ldquoDoes the level of economicgrowth influence environmental quality in Nigeria a test ofenvironmental Kuznets curve (EKC) hypothesisrdquo PakistanJournal of Social Sciences vol 7 no 4 pp 325ndash329 2010

[14] C Liu D Duan R Yu et al ldquoSpatial-temporal structure ofcoupling of the economy resources-environment system inWuhan metropolitan areardquo China Population Resources andEnvironment vol 24 no 5 pp 145ndash152 2014

[15] Z Guo Y Zheng and X Zhang ldquoAnalysis of the energy-environment-economy system in China based on dynamicCGE modelrdquo Journal of Systems Engineering vol 29 no 5pp 581ndash591 2014

[16] L Zheng and Q Zhu ldquoVertical technological progress in-dustrial structure change and sustainable economic growthunder energy and environment constraintsrdquo Journal of Fi-nance and Economics vol 7 pp 49ndash60 2013

[17] Z L Zhang B Xue X P Chen and C Y Lu ldquoEvolutionarymechanism analysis of energy-economy-environment systemin China based on Haken modelrdquo Ecological Economy(Chinese Version) vol 31 no 1 pp 14ndash17 2015

[18] Y-M Wei R Zeng and Y Fan ldquoA multi objective goal pro-gramming model for Beijingrsquos coordination development ofpopulation resources environment and economyrdquo SystemEngineering-5eory and Practice vol 22 no 2 pp 74ndash83 2002

[19] A Loschel and V M Otto ldquoTechnological uncertainty andcost effectiveness of CO2 emission reductionrdquo Energy Eco-nomics vol 31 no 31 pp S4ndashS17 2009

[20] C Erdmenger H Lehmann K Muschen J Tambke S Mayrand K Kuhnhenn ldquoA climate protection stategy for Ger-many-40 reduction of CO2 emission by 2020 compared to1990rdquo Energy Policy vol 37 pp 158ndash165 2009

[21] Y Xu and T Masui ldquoLocal air pollutant emission reductionand ancillary carbon benefits of SO2 control policies appli-cation of AIMCGE model to Chinardquo European Journal ofOperational Research vol 198 no 1 pp 315ndash325 2009

[22] J M Cullende and J M Allood ldquo-e efficient use of energytracing the global flow of energy from fuel to servicerdquo EnergyPolicy vol 38 no 1 pp 75ndash81 2010

Complexity 13

[23] M Prasad and S Munch ldquoState-level renewable electricitypolicies and reductions in carbon emissionsrdquo Energy Policyvol 45 no 45 pp 237ndash242 2012

[24] G Fang L Tian M Fu and M Sun ldquo-e impacts of carbontax on energy intensity and economic growth - a dynamicevolution analysis on the case of Chinardquo Applied Energyvol 110 pp 17ndash28 2013

[25] G Fang L Tian M Fu M Sun Y He and L Lu ldquoHow topromote the development of energy-saving and emission-reduction with changing economic growth rate-a case study ofChinardquo Energy vol 143 no 143 pp 732ndash745 2018

[26] G Fang L Tian M Fu et al ldquo-e effect of energy con-struction adjustment on the dynamical evolution of energy-saving and emission-reduction system in Chinardquo AppliedEnergy vol 196 pp 180ndash189 2017

[27] G Fang L Tian M Fu M Sun R Du and M Liu ldquoIn-vestigating carbon tax pilot in YRD urban agglomerations-Analysis of a novel ESER system with carbon tax constraintsand its applicationrdquo Applied Energy vol 194 pp 635ndash6472017

[28] X Li J Du and H Long ldquoA comparative study of Chineseand foreign green development from the perspective ofmapping knowledge domainsrdquo Sustainability vol 10 no 12p 4357 2018

[29] X Fan Y Zhang and J Yin ldquoEvolutionary analysis of a three-dimensional carbon price dynamic systemrdquo Sustainabilityvol 11 no 1 p 116 2019

[30] J-Z Wang J-J Wang Z-G Zhang and S-P Guo ldquoFore-casting stock indices with back propagation neural networkrdquoExpert Systems with Applications vol 38 no 11 pp 14346ndash14355 2011

[31] M A Boyacioglu and D Avci ldquoAn adaptive network-basedfuzzy inference system (ANFIS) for the prediction of stockmarket return the case of the istanbul stock exchangerdquo ExpertSystems with Applications vol 37 no 12 pp 7908ndash7912 2010

[32] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid modelbased on rough sets theory and genetic algorithms for stockprice forecastingrdquo Information Sciences vol 180 no 9pp 1610ndash1629 2010

[33] E Hadavandi H Shavandi and A Ghanbari ldquoIntegration ofgenetic fuzzy systems and artificial neural networks for stockprice forecastingrdquo Knowledge-Based Systems vol 23 no 8pp 800ndash808 2010

[34] A Bagheri H Mohammadi Peyhani and M Akbari ldquoFi-nancial forecasting using ANFIS networks with quantum-behaved particle swarm optimizationrdquo Expert Systems withApplications vol 41 no 14 pp 6235ndash6250 2014

[35] X Liu and X Ma ldquoBased on BP neural network stock pre-dictionrdquo Journal of Curriculum and Teaching vol 1 no 1pp 45ndash50 2012

[36] A S Babu and S K Reddy ldquoExchange Rate Forecasting usingARIMA neural network and fuzzy neuronrdquo Journal of Stockamp Forex Trading vol 4 no 3 pp 1ndash5 2015

[37] A Murkute and T Sarode ldquoForecasting market price of stockusing artificial neural networkrdquo International Journal ofComputer Applications vol 124 no 12 pp 11ndash15 2015

[38] Q Ye and L Wei ldquo-e prediction of stock price based onimproved wavelet neural networkrdquo Open Journal of AppliedSciences vol 5 no 4 pp 115ndash120 2015

[39] L Zhang F Wang B Xu W Chi Q Wang and T SunldquoPrediction of stock prices based on LM-BP neural networkand the estimation of overfitting point by RDCIrdquo NeuralComputing and Applications vol 30 no 5 pp 1425ndash14442018

[40] M Marzouk and S Azab ldquoEnvironmental and economicimpact assessment of construction and demolition wastedisposal using system dynamicsrdquo Resources Conservation andRecycling vol 82 pp 41ndash49 2014

[41] D H Meadows J Randers and D L Meadows5e Limits toGrowth5e 30-Year Update Chelsea Green Pub White RiverJunction VT USA 2004

[42] P P-J Yang and O B Lay ldquoApplying ecosystem concepts tothe planning of industrial areasa case study of SingaporersquosJurong Islandrdquo Journal of Cleaner Production vol 12no 8ndash10 pp 1011ndash1023 2004

[43] Y Fang R P Cote and R Qin ldquoIndustrial sustainability inChina practice and prospects for eco-industrial develop-mentrdquo Journal of Environmental Management vol 83 no 3pp 315ndash328 2007

[44] D Guan W Gao W Su H Li and K Hokao ldquoModeling anddynamic assessment of urban economy-resource-environ-ment system with a coupled system dynamics- geographicinformation systemmodelrdquo Ecological Indicators vol ll no 5pp 1333ndash1344 201l

[45] S F Zhan X C Zhang C Ma and W P Chen ldquoDynamicmodelling for ecological and economic sustainability in arapid urbanizing regionrdquo Procedia Environmental Sciencesvol 13 pp 242ndash251 2012

[46] I Musu and M Lines ldquoEndogenous growth and environ-mental preservationrdquoldquoEndogenous growth and environ-mental preservationrdquo in Environmental EconomicsProceeding of European Economic Association at OxfordG Boero and A Silberston Eds St Martins Press LondonUK 1995

[47] D Fullerton and S Kim ldquoEnvironmental investment andpolicy with dissortional taxes and endogenous growthrdquoJournal of Environmental Economics and Managementvol 56 no 2 pp 141ndash154 2008

[48] J-h Chen C Lai and J Y shieh ldquoAnticipated environmentpolicy and transitional dynamics in endogenous growthmodelrdquo Environmental and Resource Economics vol 25 no 2pp 233ndash254 2003

14 Complexity