A Stochastic Nonlinear Evolution Model and Dynamic Neural Coding on Spontaneous Behavior of Large-Scale Neuronal Population

Abstract

In this paper we propose a new stochastic nonlinear evolution model that is used to describe activity of neuronal population, we obtain dynamic image of evolution on the average number density in three-dimensioned space along with time, which is used to describe neural synchronization motion. This paper takes into account not only the impact of noise in phase dynamics but also the impact of noise in amplitude dynamics. We analyze how the initial condition and intensity of noise impact on the dynamic evolution of neural coding when the neurons spontaneously interact. The numerical result indicates that the noise acting on the amplitude influences the width of number density distributing around the limit circle of amplitude and the peak value of average number density, but the change of noise intensity cannot make the amplitude to participate in the coding of neural population. The numerical results also indicate that noise acting on the amplitude does not affect phase dynamics.