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

• DOI: 10.48550/arxiv.2404.11403
• Publication Date: 2024-12-01
• Authors: Daniel Cebrián-La...; Pedro Parra-Rivas; Daniel Ruiz-Reynés; Lendert Gelens
• Keywords: FitzHugh–Nagumo; Traveling waves; Cardiac systems; Spatio-temporal patterns; Neuronal dynamics; FOS: Physical sciences; Pattern Formation and Solitons (nlin.PS); Mathematical Physics (math-ph); Synchronization; Computational Physics (physics.comp-ph); Other Quantitative Biology (q-bio.OT); Nonlinear Sciences - Pattern Formation and Solitons; Pattern Formation and Solitons; Quantitative Biology - Other Quantitative Biology; Computational Physics; Bifurcation analysis; Biological Physics; Biological Physics (physics.bio-ph); Mathematical biology; Nonlinear dynamics; FOS: Biological sciences; Physics - Biological Physics; Physics - Computational Physics; Mathematical Physics

39 pages, 18 figures<br/>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.<br/>