一维Theta神经网络微分方程模型的研究——多放电行波解的存在性

Study of Modeling Differential Equations in a One-dimensional Network of Theta Neurons——The Existence of Traveling Wave Solution

研究一维theta神经元网络的微分方程模型,对该网络模型从神经元生理运动特点和微分方程本身入手进行讨论.对模型中的输入形式加以简化,证明了对任意的传播速度c>0,存在一个对应的耦合强度参数,使网络具有多放电行波解.

The model of differential equations in a one-dimensional network of theta neurons are discussed. The problem is studied from two aspects.the physiological movement characteristics of neurons and the model of differential equations. Setting assumption on the form of input and showing,in a different way,that for any wave speed c〉0,there exists a coupling strength constant among neuron cells which make this network has one traveling wave solution.