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.
arXiv comment39 pages, 18 figures
References in corpus (61)
- Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
- Photonics for artificial intelligence and neuromorphic computing
- Non-reciprocal phase transitions
- When Nonlocal Coupling Between Oscillators Becomes Stronger: Patched Synchrony or Multi-Chimera States
- Rotating Spiral Waves with Phase-Randomized Core in Non-locally Coupled Oscillators
- Discovering Symbolic Models from Deep Learning with Inductive Biases
- Robustness of chimera states for coupled FitzHugh-Nagumo oscillators
- Coherence-resonance chimeras in a network of excitable elements
- Pattern Formation in Dissipative Nonvariational Systems: The Effects of Front Bifurcations
- Time-delayed feedback in neurosystems
- Chimera states in brain networks: empirical neural vs. modular fractal connectivity
- Solitary and Coupled Semiconductor Ring Lasers as Optical Spiking Neurons
- Semi-passivity and synchronization of diffusively coupled neuronal oscillators
- Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities
- Dynamics of Elastic Excitable Media
- Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications
- Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling
- Non-reciprocity across scales in active mixtures
- Interface Proliferation and the Growth of Labyrinths in a Reaction-Diffusion System
- FitzHugh-Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena
- Noise Induced Complexity: From Subthreshold Oscillations to Spiking in Coupled Excitable Systems
- Chimera patterns in two-dimensional networks of coupled neurons
- Regime shifts in models of dryland vegetation
- Anticipating the response of excitable systems driven by random forcing
- Transitions between patterned states in vegetation models for semi-arid ecosystems
- Extreme events in Fitzhugh-Nagumo oscillators coupled with two time delays
- Phase-space geometry of mass-conserving reaction-diffusion dynamics
- A Nonlocal Contour Dynamics Model for Chemical Front Motion
- Resonance tongues and patterns in periodically forced reaction-diffusion systems
- Symmetry-breaking transitions in networks of nonlinear circuit elements
- Homoclinic Orbits of the FitzHugh-Nagumo Equation: Bifurcations in the Full System
- Emergent global oscillations in heterogeneous excitable media: The example of pancreatic beta cells
- Characterization of the anticipated synchronization regime in the coupled FitzHugh--Nagumo model for neurons
- Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators
- Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization
- Nonreciprocal Cahn-Hilliard model emerges as a universal amplitude equation
- The Dynamics of Curved Fronts: Beyond Geometry
- On the Origin of Traveling Pulses in Bistable Systems
- Structure of Cell Networks Critically Determines Oscillation Regularity
- Synchronization of coupled neural oscillators with heterogeneous delays
- Hubs, diversity, and synchronization in FitzHugh-Nagumo oscillator networks: Resonance effects and biophysical implications
- Delay-induced chimeras in neural networks with fractal topology
- First order phase transitions and the thermodynamic limit
- Generation of finite wave trains in excitable media
- Delay engineered solitary states in complex networks
- Formation of localized states in dryland vegetation: Bifurcation structure and stability
- Snaking branches of planar BCC fronts in the 3D Brusselator
- Stationary broken parity states in active matter models
- Canards Existence in FitzHugh-Nagumo and Hodgkin-Huxley Neuronal 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
- Wave propagation in spatially modulated tubes
- A general model for vegetation patterns including rhizome growth
- Phase Dynamics of Nearly Stationary Patterns in Activator-Inhibitor Systems
- Patterns, localized structures and fronts in a reduced model of clonal plant growth
- 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
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- Extreme events at the onset of epileptic-like intermittent activity of FitzHugh-Nagumo oscillators on small-world networks
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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