Nonlinear stochastic models of neurons activities

Abstract

In this paper we propose a new nonlinear evolution model of neuronal activities to obtain the average number density, which is used to describe neurocommunication among populations of neurons. The average number density is a function of the amplitude, phase and time. The number density of the diffusion process of neurocommunication is given for the active states of two populations of coupled oscillators under perturbation by both periodic stimulation and random noise. It is emphasized that the oscillatory coupling strengths and initial conditions within and between two populations of neurons are very important for investigating the mechanism of the transmission process. Particularly, the model presented in this paper can be used to describe the evolution process of the amplitudes in activities of multiple interactive populations of neurons.