Dynamics Of Moment Neuronal Networks Based On IF Model With Renewal Stochastic Inputs

Although single neuron models with random inputs have been widely stn-dide in theory and experiment.most such studies are done under the assumption that inputs are Poisson processes.Because spike trains which neuron fire and receive are commoly renewal processes.The assumption is a very rough approximation of physiological data. We will consider the case of renewal process input,which represents a more accurate approximation of synaptic inputs.Besides,in recent years,many researches are found that the spike activity of a neuron is decided not only by the mean rate,but also by higher order statistics of its input. Consider,for instance,a neuron which receives inhibitory and excitatory stochastic inputs of cqual rate.Due to the fluctuations of the input,the membrane potential may occasinally cross the threshold for spiking,thereby contradicting the basic assumptions of the arificial neural networks.This simple example illystrates that it is no much use in understanding the behaviour of real nervous systems,in that it comoletely discards the "noisy" nature of the neural code.In this paper,the issue how to approximate the integrate-and-fire(IF) with renewal inputs is studied and the MNN framework is developed according to the UAS approximation scheme for IF model.A series of new results are obtained. The main contents as follows:Chapter 1 introduces the background of the problem-researching.the recent development of the neuron model and some research results we have obtained in this field;Chapter 2 makes theoretic and numerical analysis to the HH model and IF model, and extended IF models;Chapter 3 focuses on the issue how to approximate the integrate-and-fire model with stochastic renewal inputs,two novel approximation schemes(UAS,OUS) are proposed;Chapter 4 developes a MNN framework according to the UAS approximation scheme. Within this framework,the behavior of the system of spiking neurons is specified in terms of the first- and second-order statistics of their in-terspike intervals,i.e., the mean,the variance,and the cross correlations of spike activity.It will be better to deal with the "noisy".