Definition
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...
References
Desroches M, Krupa M, Rodrigues S (2013) Inflection, canards and excitability threshold in neuronal models. J Math Biol 67(4):989–1017
FitzHugh R (1955) Mathematical models of threshold phenomena in the nerve membrane. Bull Math Biophys 17(4):257–278
FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1:445–466
FitzHugh R (1968) Motion picture of nerve impulse propagation using computer animation. J Appl Physiol 25(5):628–630
Guckenheimer J, Oliva R (2002) Chaos in the Hodgkin–Huxley model. SIAM J Appl Dyn Syst 1(1):105–114
Izhikevich EM, FitzHugh R (2006) FitzHugh–Nagumo model. Scholarpedia 1(9):1349
Keener JP, Sneyd J (2009) Mathematical physiology: I: cellular physiology, vol 1. Springer, New York
McKean HP (1970) Nagumo’s equation. Adv Math 4(3):209–223
Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35(1):193–213
Nagumo J, Arimoto S, Yoshizawa S (1962) An active pulse transmission line simulating nerve axon. Proc IRE 50(10):2061–2070
Rowat PF, Selverston AI (1997) Oscillatory mechanisms in pairs of neurons connected with fast inhibitory synapses. J Comput Neurosci 4:103–127
Scott AC (1975) The electrophysics of a nerve fiber. Rev Mod Phys 47(2):487–535
Tonnelier A (2003) The McKean’s caricature of the FitzHugh-Nagumo model I. The space-clamped system. SIAM J Appl Math 63(2):459–484
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Sherwood, W.E. (2014). FitzHugh–Nagumo Model. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_147-1
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DOI: https://doi.org/10.1007/978-1-4614-7320-6_147-1
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