Some recent progress on standing waves of FitzHugh–Nagumo system

Abstract

The FitzHugh–Nagumo system is a well-known reaction-diffusion model for exhibiting self-organized patterns. Besides regular patterns found in a neighborhood of Turing's instability, localized structures are also observed in experiment and numerical simulation. In particular, fronts and pulses are the most well-known localized structures in reaction-diffusion systems. This article is aimed at some recent results on the variational approach for studying standing waves of FitzHugh–Nagumo system.