Existence and Stability of Traveling Fronts in a Lateral Inhibition Neural Network

Abstract

We consider the existence and stability of traveling front solutions of a neural network consisting of a single layer of neurons synaptically connected by lateral inhibition. For a specific “Mexican Hat” coupling function, the existence condition for traveling fronts can be reduced to the solution of an algebraic system. Our work extends the existence of traveling fronts of the classic Amari model by considering a nonsaturating piecewise linear gain function. We further establish an analytic method to investigate the linear stability of traveling front solutions in the Heaviside gain case.