1. Stochastic Bursting Synchronization in a Population of Subthreshold Izhikevich Neurons
Woochang Lim1 and Sang-Yoon Kim2
1Department of Science Education, Daegu National University of Education
2Department of Physics, Kangwon National University
Introduction
 Representative Bursting Neurons
Cortical Bursting Neurons,
Thalamocortical relay neurons,
Thalamic recticular neurons,
Hippocampal pyramidal neurons,
Purkinje cells in the cerebellum Bursting of cat visual cortical neuron
 Three major Hypotheses on the Importance of Bursting in Neuroscience
(1) Burstings are necessary to overcome the synaptic transmission failure.
(2) Burstings can transmit saliency of the input because the effect of bursting
on the postsynaptic neuron is stronger than a single spike.
(3) Burstings can be used for selective communication between neurons,
where the interspike frequency within the bursts encodes
the channel of communication.
Emergence of Collective Coherence
 Thermodynamic Order Parameter
Global Potential:
Mean Square Deviation of VG:
As N  then O  non-zero (zero)
limit value for coherent (incoherent)
states.
Incoherent State Coherent State Incoherent State
Globally-Coupled Excitatory Izhikevich Neurons
Stochastic Bursting Synchronization
 Burst and Spike Synchronization
Hedgehog-Like Limit Cycle with Spines
 Burst Synchronization without Spike Synchronization
Loss of Spike Synchronization in Each Burst Band
Regular Limit Cycle without Spines
Parameters for regular-spiking cortical excitatory neuron: a=0.02, b=0.2,
c=-65, d=8
Parameters for excitatory synapse: =10, =0.5,
Vsyn=10, v*=0, =2
Spiking in the Single Izhikevich Neuron
 Firing Transition in the Single Izhikevich Neuron
Transition to firing occurs IDC=I*DC (~3.78)
IDC < I*DC: Resting state; IDC>I*DC: Spiking state
Mean firing rate IDC= IDC=3.9
 Individual Neurons Exhibit Noise-Induced Bursting.
Two Kinds of Spike and Burst Synchronization Occurs,
In Contrast to Spiking Neurons Showing Only Spike Synchronization.
 Characterization of Degree of Stochastic Bursting Synchronization
 Noise-induced Spiking in the Subthreshold
Izhikevich Neuron for IDC=3.6
Characterization of Synchronization Degree
 Synchronization Measure
Measuring the degree of resemblance
between the global and individual
output signals
Bursting in Individual Neurons
 Transition from Spiking to Bursting in Individual Neuron
for IDC=3.6 & D=0.5
J<J* (~0.57): Individual neurons exhibit spikings.
J>J*: Individual neurons exhibit burstings.
Increase in J, No. of spikes in the burst increases.
Summary
 Emergence of Stochastic Bursting Synchronization in An Intermediate Range
of Noise Intensity
 Associated with Cognitive Brain Rhythms (sensory perception, multisensory
integration, selective attention, working memory)