Six decades of the FitzHugh-Nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines

TL;DR

This review comprehensively explores six decades of research on the FitzHugh-Nagumo model, highlighting its diverse spatio-temporal behaviors and broad interdisciplinary applications, including new stability and bifurcation analyses.

Contribution

It provides a detailed catalog of dynamical states, bifurcations, and extends previous work with stability and bifurcation analyses for coupled spatial systems.

Findings

Catalogs known dynamical states and bifurcations

Addresses complex phenomena like traveling waves and patterns

Provides new stability and bifurcation analyses for coupled systems

Abstract

The FitzHugh-Nagumo equation, originally conceived in neuroscience during the 1960s, became a key model providing a simplified view of excitable neuron cell behavior. Its applicability, however, extends beyond neuroscience into fields like cardiac physiology, cell division, population dynamics, electronics, and other natural phenomena. In this review spanning six decades of research, we discuss the diverse spatio-temporal dynamical behaviors described by the FitzHugh-Nagumo equation. These include dynamics like bistability, oscillations, and excitability, but it also addresses more complex phenomena such as traveling waves and extended patterns in coupled systems. The review serves as a guide for modelers aiming to utilize the strengths of the FitzHugh-Nagumo model to capture generic dynamical behavior. It not only catalogs known dynamical states and bifurcations, but also extends previous studies by providing stability and bifurcation analyses for coupled spatial systems.