Stein神经元模型在共同的随机输入下的同步性

主要证明了脉冲幅度与神经元状态有关的Stein模型都能够使两个初始膜电位不同的神经元以概率1达到同步发放.这一结论可以推广到多个初始膜电位不同的神经元.但同步发放的时间没有上限,目前只能给出一个粗略的方法,估计出同步概率在α%(0 <α<100)以上的同步时间.最后,脉冲幅度与神经元状态有关的Stein模型的数值模拟结果符合前述结论的预期.

Synchronization in Stein's Model with Magnitude-Variant Inputs Evoked by Common Stochastic Stimuli

Synchronization among neurones is a widely observed phenomenon. Integrate-and-Fire model(I-F model) is one of the most famous model characterizing the membrane potential of a neuron. Stein's model is the stochastic version of I-F model, whose inputs are Poisson impulses. It is reliable that Stein's model with magnitude-variant input will make 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. However,there is no upper boundary of the firing time according to Stein's model. Only a rough estimation can be got to estimate the upper boundary of synchronization time when the probability of synchronization is equal or greater than α%(0<α<100).Finally an effective algorithm is employed to simulate this type of Stein's model with magnitude-variant input. The simulation results coincide with our expectation.