Stein, Neuron Model Synchronization, Common Random Input

It is well known that synchronization among neurones is a widely observed and studied phenomenon.Integrate-and-Fire model(I-F model) is one of the most useful model characterizing the membrane potential of a neuron.Stein's model is the stochastic version of I-F model,whose inputs are Poisson impulses.In this paper we proved that Ornstein-Uhlenbeck Process(OUP) diffusion approximation of Stein's model cannot make two identical neurones with different initial membrane potentials fire synchronously. Furthermore we confirmed that two types of Stein's model will let two identical neurones with different initial membrane potentials fire synchronously with probability 1.The same conclusion is available to a group(more than two) of identical neurones.This conclusion can be reached because of the common stochastic stimuli-Poisson pulses.But theoretically speaking there is no upper boundary of the firing time which is a stopping time actually.We still give an approach to estimate the synchronization time when the probability of synchronization is equal or greater thanα%(0＜α＜100).Finally we simulated Stein's model with an effective algorithm. The simulation results coincide with our expectation.