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Globally-Coupled Excitatory Izhikevich Neurons
Coupling-Induced Population Synchronization in An Excitatory Population of Subthreshold Izhikevich Neurons
Woochang Lim1 and Sang-Yoon Kim2
1Department of Science Education, Daegu National University of Education2Research Department, LABASIS Co.
Summary Appearance of Rich Population States by Changing the Coupling Strength Incoherent State Spike Synchronization Burst Synchronization Incoherent State Fast Spike Synchronization Incoherent State Non-firing State
Emergence of Three Types of Population Synchronization Spike, Burst, and Fast Spike Synchronization
Future Works: Brain Rhythm Emerging via Population Synchronization in the Complex Neural Network such as Small-World and Scale-Free Neural Networks
Transition to Non-Firing State via Stochastic Oscillator Death
Average Population Spike Rate R
As N then R non-zero (zero) limit value for firing (non-firing) states.
Non-firing states appear due to the stochastic oscillator of individual neurons
Various Transitions in Individual Behaviors
Transition from Spiking to Bursting As J increases, average number of spike <n> per burst becomes larger than unity. Transition from spiking to bursting With further increase in J, <n> increases.
Transition from Bursting to Fast Spiking With increase in J, burst length becomes longer Eventually average burst length divers to the infinity. Transition to the Fast Spiking State
Transition from Fast Spiking to Oscillator Death As J increases, slow spikings with longer spiking phases appear and mean firing rate goes to zero. Occurrence of Stochastic Oscillator Death
Population Coherent and Incoherent States
Appearance of Rich Population States by Changing the Coupling Strength
Global Potential VG & Global Recovery Variable UG:
Incoherent State Spike Synchronization Burst Synchronization Incoherent State Fast Spike Sync. Incoherent State Non-firing State
Thermodynamic Order Parameter Mean Square Deviation of VG:
As N then O non- zero (zero) limit value for coherent (incoherent) states.
Three Types of Population Synchronization
Spike Synchronization Burst Synchronization Stripes appear regularly Clear burst bands, composed of stripes, in the raster plot. appear successively. VG shows a small-amplitude VG exhibits a large-amplitude bursting rhythm. Rhythms.
Fast Spike Synchronization Stripes appear successively at short time interval in the raster plot. VG shows a small-amplitude fast rhythm.
Introduction Brain Rhythm Emerging via Population Synchronization Brain Rhythm emerge via synchronization between individual firings. Population Synchronization between neural firings may be used for efficient sensory and cognitive processing. Population Synchronization is also correlated with pathological rhythms associated with neural diseases.
Population Synchronization in Neural Network of Suprathreshold Neurons Individual Neurons: Regular Firings like Clocks
Population Synchronization in Neural Network of Subthreshold Neurons Individual Neurons: Intermittent and Stochastic Firings like Geiger Counters Noise-Induced Population Synchronization in a Population of Subthreshold Neurons
Regular-Spiking (RS) Cortical Excitatory Neuron
Firing Transition in the Single Izhikevich Neuron Transition to firing occurs IDC=I*DC (~3.78) RS Izhikevich neuron shows type-II excitability. IDC < I*DC: Resting state; IDC>I*DC: Spiking state
Complex Noise-induced Spiking with Irregular Interspike Intervals in the Subthreshold Izhikevich Neuron for IDC=3.6
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