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

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