Integrate-and-Fire Model With Inputs On Inverse Gaussian Distribution

IF model was early studied abroad .After Lapicque proposed IF model ,single neuron models with random inputs have been widely studied.But most such studies are done under the assumption that inputs are Poisson processes ,The assumption is a very rough approximation of physiological data. We will consider the case of renewal process(the Inverse Gaussian distribution) inputs which conform with physiological models.We adopted firstly two better approximations on the basis of the previous in this paper. That is ,to find a same mean and variance process with a synaptic approximations ,Then we do a lot of numerical simulation to simulate IF model with the Inverse Gaussian inputs. The network synchronizes through simple layers,That is,the inputs and outputs obey the same distribution,better than ever Poisson inputs.In this paper,the main results as follows :The first chapter introduces study background of the neural network, prior knowledge and the main results in the paper.The second chapter introduces the structure of the neuron ,neuronal information firing theory,Hodgkin-Huxley(HH) model,Integrate-and-Fire(IF) model and simulation of both model with stable inputs.The next two chapters are the main content.In the third chapter we derive the corresponding UAS and OUS approximating schemes.Then we show that the output spike trains generated by IF model.By the continuous approximations,we conclude that both schemes work reasonably well.In the forth chapter we consider the output spike trains by the IF model.By simulation we find out both schemes work well ,Finally we develop our MNNs framework based on them.