Phase Response Synchronization in Neuronal Population with Time-Varying Coupling Strength.

Xianfa Jiao,Wanyu Zhao,Jinde Cao

doi:10.1155/2015/816738

Abstract

We present the dynamic model of global coupled neuronal population subject to external stimulus by the use of phase sensitivity function. We investigate the effect of time-varying coupling strength on the synchronized phase response of neural population subjected to external harmonic stimulus. For a time-periodic coupling strength, we found that the stimulus with increasing intensity or frequency can reinforce the phase response synchronization in neuronal population of the weakly coupled neural oscillators, and the neuronal population with stronger coupling strength has good adaptability to stimulus. When we consider the dynamics of coupling strength, we found that a strong stimulus can quickly cause the synchronization in the neuronal population, the degree of synchronization grows with the increasing stimulus intensity, and the period of synchronized oscillation induced by external stimulation is related to stimulus frequency.

Highlights

A nervous system’s response to external stimulus can provide crucial information about its dynamical properties
The dynamic models of globally coupled phase oscillators have been proposed for the study of neuronal synchronization in the brain [10,11,12,13,14]
The dynamics of globally coupled neuronal oscillators with varying coupling strengths have been investigated in recent years [15, 16, 18,19,20]

Summary

Introduction

A nervous system’s response to external stimulus can provide crucial information about its dynamical properties. The phase sensitivity function can quantitatively illuminate how an external stimulus affects the timing of spikes immediately after the stimulus in repetitively firing neurons, and it is an important and effective method to study the dynamic behavior of synchronous activity in nervous system [1,2,3,4,5]. We investigate the effect of time-periodic coupling strength on the synchronized behaviors of neuronal population subjected to external harmonic stimulus by the use of phase sensitivity function. In this paper, based on phase response model of population of coupled neuronal oscillators, we consider the dynamics of the coupling strength in order to explore the effect of external stimulus on synchronized oscillation in neuronal population

Model Equations

Numerical Simulations

Conclusions