Encyclopedia of Computational Neuroscience

Living Edition
| Editors: Dieter Jaeger, Ranu Jung

FitzHugh–Nagumo Model

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7320-6_147-1


The FitzHugh–Nagumo (FHN) model is a mathematical model of neuronal excitability developed by Richard FitzHugh as a reduction of the Hodgkin and Huxley’s model of action potential generation in the squid giant axon (FitzHugh 1955). Nagumo et al. subsequently designed, implemented, and analyzed an equivalent electric circuit (Nagumo et al. 1962).

In its basic form, the model consists of two coupled, nonlinear ordinary differential equations, one of which describes the fast evolution of the neuronal membrane voltage, the other representing the slower “recovery” action of sodium channel deinactivation and potassium channel deactivation. Phase plane analysis of the FHN model provides qualitative explanations of several aspects of the excitability exhibited by the Hodgkin–Huxley (HH) model, including all-or-none spiking, excitation block, and the apparent absence of a firing threshold. A version of the FHN equations which adds a spatial diffusion term models the propagation of an...


Travel Wave Solution Relaxation Oscillation Tunnel Diode Threshold Curve Phase Plane Analysis 
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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.University of UtahSalt Lake CityUSA