Existence and Asymptotic Behaviors of Traveling Wave Solutions for the FitzHugh–Nagumo System

ABSTRACT In this paper, we are concerned with the existence of traveling wave solution for FitzHugh–Nagumo system, which is an excitable model for studying nerve impulse propagation. By using traveling wave transformation and time scale transformation, the FitzHugh–Nagumo system is transformed into a singularly perturbed differential system. We construct a locally invariant manifold for the associated traveling wave equation and obtain the existence of traveling wave solution by employing geometric singular perturbation theory and Fredholm orthogonality. Furthermore, we also discuss the asymptotic behaviors of the traveling wave solution by applying the asymptotic theory.