一维Theta神经网络中扰动后多放电行波解存在性

Regular traveling waves after perturbatiom in a one-dimensional network of Theta neurons

主要研究一维Theta神经元网络的微分方程模型,从神经元生理运动特点和微分方程入手对该网络模型进行研究.对模型中的输入形式进行简化,给输入一个扰动,证明了扰动后多放电行波解的存在性.

The model of differential equations in a one-dimensional network of Theta neurons is discussed. The prob- lem is studied from two aspects., the physiological movement characteristics of neurons and the model of differential equations. By setting assumption on the form of input, this paper proves that under small extra perturbation, there exists two traveling wave solutions which spike more than one time.