A study of the FitzHugh-Nagumo Model with diffusion term

Abstract

This article aims to provide a theoretical background for the FitzHugh-Nagumo Model, a reaction-diffusion system originating from the field of neuroscience modeling. We begin by examining a linear reaction-diffusion system, establishing conditions under which Hopf bifurcations exist. We then bridge these findings to the nonlinear and nonhomogeneous FitzHugh-Nagumo (nhFHN) system, demonstrating the conditions necessary for generating oscillatory behavior in this system. Finally, we present numerical simulations of the nhFHN system.