Six decades of the FitzHugh-Nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines
arXiv:2404.11403 · doi:10.1016/j.physrep.2024.09.014
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.
39 pages, 18 figures
References in corpus (20)
- Photonics for artificial intelligence and neuromorphic computing
- Discovering Symbolic Models from Deep Learning with Inductive Biases
- Robustness of chimera states for coupled FitzHugh-Nagumo oscillators
- Time-delayed feedback in neurosystems
- Non-reciprocity across scales in active mixtures
- FitzHugh-Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena
- Symmetry-breaking transitions in networks of nonlinear circuit elements
- Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators
- Nonreciprocal Cahn-Hilliard model emerges as a universal amplitude equation
- Hubs, diversity, and synchronization in FitzHugh-Nagumo oscillator networks: Resonance effects and biophysical implications
- Generation of finite wave trains in excitable media
- Stationary broken parity states in active matter models
- Traveling pulses in Class-I excitable media
- Bifurcation structure of traveling pulses in Type-I excitable media
- Transitions between dissipative localized structures in the simplified Gilad-Meron model for dryland plant ecology
- Solitary states in complex networks: impact of topology
- Analytical approximations for the speed of pacemaker-generated waves
- Neuron-like spiking dynamics in the asymmetrically-driven dissipative photonic Bose-Hubbard dimer
- Enhancing model identification with SINDy via nullcline reconstruction
- Ghost cycles exhibit increased entrainment and richer dynamics in response to external forcing compared to slow-fast systems
Cited by in corpus (4)
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- Enhancing model identification with SINDy via nullcline reconstruction
- Hyperparameter Optimization in the Estimation of PDE and Delay-PDE models from data