The Study of Modeling Differential Equations in a One-Dimensional Network of Theta Neurons

This paper focuses on the modeling differential equations in a one-dimensional network of theta neurons. The problem is studied from two aspects: the physiological movement characteristics of neurons and the modeling differential equations. At first, we simplify the computational models for synaptically coupled networks of neurons in order to obtain the regular traveling waves in a one-dimensional network of theta neurons. Then we set assumption on the form of input. Thus, we can show, in a different way, that for any wave speed, there exists a coupling strength such that there exists one traveling wave solution for this network. Moreover, we proved that under small extra perturbation, there exists two traveling wave solutions which spike more than one time.