The Invariant Distribution Based On Moment Neuronal Networks

During the past 20 years, we have witnessed the development of the artificialneuronal networks theory and its more and more impact on Neuroscience and en-gineering applications. One of the central topics in Computational Neuroscienceis the coding problem,that is to say, how does the nervous system encode and thendecode information,from then on,theories of coding in the nerevous system focusedon rate coding applied by HH and IF model,as in conventional neural network the-ory. In this paper,we mainly discussed the stability of the neuronal networks byconstructing suitable models based on this type of encode.In recent years,many researches are found that the spike activity of a neuronis decided not only by the mean rate, but also by higher order statistics of its input.Consider,for iustance,a neuron which receives inhibitory and excitatory stochasticinputs of equal rate.Due to the fluctuations of the input,the membrane potentialmay occasinally cross the threshold for spiking, thereby contradicting the basic as-sumptions of the arificial neural networks.This simple example illystrates that itis no much use in understanding the behaviour of real nervous systems, in that itcomoletely discards the "noisy" nature of the neural code.In this paper, the main results as follows:(1). Made theoretic and numerical analysis to the HH model and IF model,and ex-tended two models;(2). Constructed a new neuronal networks model. It is considered not only the firstand the second moment, and possibly higher order statistics of firing. It will be bet-ter to deal with the "noisy". Because we consider the moments of the firing,we callmoment neuronal networks model;(3). Based on the moment neuronal networks,if Poisson process inputs it,its outputwon't be Poisson process. So, in this paper, we considered the stability of the moment neuronal networks with renewal processes inputs. That is to say, whether has theuniformity between the inputs and the outputs.