Upload
stephanie-morgan
View
249
Download
4
Tags:
Embed Size (px)
Citation preview
Complex System Science
John Finnigan
CSIRO Atmospheric Research
Contents
• Complex systems Science• Systems• Complexity-the idea of emergent structure• Farming systems as ‘Complex Adaptive Systems’
• Three Approaches to Understanding• Network Theory• Cellular Automata• Agent Based Models
• Summary• The CSIRO Centre for Complex Systems
Science
Complex System Science
Has two elements:
• Systems-collections of interacting things
• Complexity-the essence of which is the property of self-organisation or emergence of structure from the interaction between the constituent parts of the system
Emergence or Self-Organisation
•We recognise this phenomenon over a vast range of physical scales and degrees of complexity
•From Galaxies ~ 106 Light Years
To cyclones
~ 100 km
And Chemical reactions ~ 10 cm
Ribosome
E Coli
Root Tip
Amoeba
To Gene expression and cell interaction
The processing of information by the brain
To animal societies and the
emergence of culture
And the social artefacts of human society such as economies
The Concept of Self-Organisation has consequences at several levels
• At the whole system level (in the present case, farming systems) it means that ‘no one is in charge’ and optimal or command and control solutions to system problems usually fail (sooner or later)
• At the level of analysis, self organising processes provide us with powerful tools
Foot and Mouth Disease in the UK An example of failure caused by focussing on one part of the system and ignoring the links between biophysics and economics
Economic rationalization of abattoirs and bizarre EU subsidies increased the connections between herds to a critical point.
Changes to F&M reporting rules may have delayed the isolation of infectious animals.
The relationship between these actions and the epidemiology of F&M was not appreciated in advance (at least where it mattered) because the livestock industry was not viewed as an integrated system.
Farming Systems at the gross level involve Economics, People, their Social Networks as well as Biophysics such as hydrology,
soil science, Agronomy and Biology.
• We can attempt to understand and model the whole system or parts of it
• To model the whole system we need first a mental map and then some techniques to capture the parts and interactions of the mental map
The MarketClimate
A regional scale social-ecological system including farming, as a complex adaptive system
In a CAS, there is no Fat Controller. The system behaviour is an emergent property
Illustrative Examples of Dynamic Process Interactions
Argonne National Laboratory
NATURALPROCESSES
SOCIETALPROCESSES FORMATION
OF ELITES
LONGDISTANCE
TRADE
IRRIGATION
WEATHER &CLIMATE
DIFFERENTIATIONOF ROLES
HOUSEHOLDMGMT.
SOILCONDITION
TOWNFORMATION
STATEFORMATION
SURFACEEXCHANGE
EVOLUTION OFHOUSEHOLDS
DEMO-GRAPHICS
CONFLICT
KINSHIP-BASED
BEHAVIORS
AGRICULTURE
HYDROLOGY
PLANTGROWTH
The simulation framework implementsan "agent-based" simulation in whichdozens to thousands of Households
interact and conduct their activities in anenvironment that responds to their
actions and updates itself daily.
Modeled Households can respond toenvironmental stress (repeated droughts, etc.) by,for example:
violating fallow (plant each field, each year) manuring fields clearing more distant fields shifting emphasis toward pastoralism importing food, emigrating, etc.
MM5Mesoscale
WeatherModel
AtmosphereObject
(one of manyalternativemodels)
EPIC includes: crop growth soil condition soil erosion nutrient
cycling, etc.
SWAT/EPIC
Crop Model
FieldObjects
Decide Crop Strategy
Cultivate Crop
Borrow Grain
Obtain Plow Team
Release Field to Forage
HouseholdObjects
Societal ProcessSimulation Models
Natural ProcessSimulation Models
... many others, basedon historical records...
... and cultural analogs
generally severalFields per Household
Objects and Associated Models
Argonne National Laboratory
We can build models of Complex adaptive Systems using techniques like ‘Agent based Modelling’ but to understand and predict their
behaviour, we need a science of systems
The understanding we need is coming from a evolving blend of at least three different approaches:
1. Dynamical Systems Theory
2. Network Theory
3. Evolutionary or adaptive computing
1 Studying Ecosystems as dynamical systems
A minimal model of an ecosystem describes the change over time of ecosystem state.
The trajectories indicate stable states of the ecosystem as external conditions change
Ecosystems that display two (or more) alternative stable states include :
•lakes(oligotrophic/eutrophic),
• grasslands/woodlands,
•coral reefs (pristine/algal covered),
•marine ecosystems as measured in fish catch….
(Figs from Scheffer et al, 2001, Nature)
Basins of attraction and Ecosystem Resilience
A minimal model of an ecosystem describes the change over time of an unwanted ecosystem property, x such as lake turbidity
a represents an environmental factor that promotes x, b represents the rate at which x decays in the system, r is the rate at which x recovers again as a function f of x
The form of f(x) determines whether multiple stable states or attractors will exist
dxa bx r f x
dt
p p pf x x x h
(Figs from Scheffer et al, 2001, Nature)
What do we mean by stable states?
Linear dynamics Non-linear dynamics Boundaries of Strange
Periodic attractor Strange Attractor Attractors are Fractal
2 We can represent most systems as networks with interactions across the links-
Network Topologies control System behaviour
Regular Network: each node has the same number of connections
Homogeneous network: Number of connections per node varies but there is a clear average value. Networks like this can result from randomly connecting nodes. Near the phase transition they are vulnerable to random removal of links
Heterogeneous or ‘scale free’ network: There is no average number of connections per node: Living networks that grow by accretion often have this dendritic form. They are resilient to random removal of links but vulnerable to a targeted attack that removes a key node
3 Adaptive Systems can be illustrated simply using Cellular Automata. CAs are Systems that evolve
on lattices according to local interaction rules
The simplest rules: the state of a cell at time T+1 is determined by its own state and that of its two neighbours at time T
Discretization of PDEs yields Cellular Automata
2 1 1y
y yx
2
21 2 0 1
yy y y
x
2
2
y y y
t x x
Advection-diffusion equation
t=n
t=n+1
-1 0 +1X=
We can form new types of Cellular Automata by changing the interaction rules or the wiring or both
T=0
T=1
T=2
Dynamics on networks can evolve either by changes in the interaction rules
Or by changes in the ‘wiring’ of the network
The Cellular Automaton as a computer:Evolving the local rules that will perform a
computational task by applying a global selection pressure
T=0
T=1
T=2
The colour that a cell adopts at the next timestep depends only on the colours of itself and its neighbours at the present time step
Rules are recombined (bred) and selected according to Darwinian principles to find the set of local rules that will solve the density problem
Moving Away from Classical Mathematics
• With complete freedom to stipulate rules and wiring between elements of our CAs in the virtual world of the computer and then to let them evolve as part of the computation, we can form mathematical objects that are very difficult to capture using the approaches of conventional mathematics but which match very well what we observe in living systems.
• Agent Based Models exploit this freedom• Analysis using network theory and similar techniques is
leading to increasing understanding of these systems-but so far we have few general principles
Summary
• Complex Systems Science brings together systems approaches and a rapidly developing science of systems
• Rather than being any particular set of techniques it is primarily the adoption of a different point of view
• That is, to admit the prevalence of self- organisation in complex systems together with the behaviours that flow from that and the techniques necessary to study it.
The CSIRO Centre for Complex Systems Science-A Virtual Centre
The Core Group comprises a permanent Science Director, a Communication and Training Manager, Post Docs, PhDs and visitors. It interacts with Division based projects to do basic research in CSS.
Projects are located within CSIRO Divisions (and partner Institutions).
A key function of the Core group is to manage interaction between the projects. The Core and the Division-based Projects are closely networked.
The Compass of Complex System Science: Projects in the CSIRO Centre for CSS-1
• Inference of complex systems properties from fragmentary information (Mantle dynamics and mineralization: State Space reconstruction)
• Ensemble Prediction of Atmospheric and Ocean-Atmosphere Regime Transitions (Dynamical Systems theory)
• The stability of the Southern Ocean overturning circulation (Dynamical Systems theory)
• Critical states in bushfires (Dynamical Systems theory, Agent Based Modelling)
• The effects of model structure and dimensionality on the emergent properties of ecosystem models (Estuarine systems: Dynamical Systems theory, ABM)
• Rapid shifts in state and resilience in river systems (ABM)
• Targeting Drug-like properties in Chemical libraries (Genetic Algorithms, Evolutionary computing)
The Compass of Complex System Science: Projects in the CSIRO Centre for CSS-2
• Tracking Air Borne Chemical Signals (Fractal turbulence + AI, ABM)
• Adaptation and resilience in regional socio-economic systems (Managed rangelands: ABM)
• Multiscale modelling in Industrial and Natural systems (Lattice-Boltzmann methods, Non-Equil Thermodynamics)
• Interactions, information sharing and simulated reasoning of fishers in an agent-based, Bayesian network model of fishing behaviour (ABM)
• The Future of the Swan River: Governance and Agent Based Modeling (ABM, Evolutionary game theory)
• Our National Electricity Market as a Complex Adaptive System (ABM)
• Links between resilience and information in complex adaptive systems (ABM, Evolutionary game theory)
The Purpose of This Workshop
• Is to bring together workers with awareness of the problems and workers with knowledge of CSS Techniques
• And to start a process of developing projects for future joint funding
• We plan a funding round built around the 2nd CSIRO CSS workshop in Sydney 27-29 August, 2003.