Stability of Traveling Fronts in a Neural Field Model

Abstract

We investigate the stability of traveling front solutions in the neural field model. This model has been studied intensively regarding propagating patterns with saturating Heaviside gain for neuron firing activity. Previous work has shown the existence of traveling fronts in the neural field model in a more complex setting, using a nonsaturating piecewise linear gain. We aimed to study the stability of traveling fronts in the neural field model utilizing the Evans function. We attained the Evans function of traveling fronts using an integration of analytical derivations and a computational approach for the neural field model, with previously uninvestigated piecewise linear gain. Using this approach, we are able to identify both stable and unstable traveling fronts in the neural field model.