- 13-91 Gianni Arioli, Hans Koch
- Existence and stability of traveling pulse solutions
of the FitzHugh-Nagumo equation
(1086K, plain TeX, with eps figures)
Nov 27, 13
(auto. generated ps),
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Abstract. The FitzHugh-Nagumo model is a reaction-diffusion equation
describing the propagation of electrical signals
in nerve axons and other biological tissues.
One of the model parameters is the ratio ε of two time scales,
which takes values between <i>0.001</i> and <i>0.1</i> in typical simulations
of nerve axons.
Based on the existence of a (singular) limit at ε<i>=0</i>,
it has been shown that the FitzHugh-Nagumo equation admits
a stable traveling pulse solution for sufficiently small ε<i>>0</i>.
In this paper we prove the existence of such a solution for ε<i>=0.01</i>.
We consider both circular axons and axons of infinite length.
Our method is non-perturbative and should apply
to a wide range of other parameter values.