Title: Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation
Authors: G. Arioli, H. Koch
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 0.001 and 0.1 in typical simulations of nerve axons. Based on the existence of a (singular) limit at ε=0, it has been shown that the FitzHugh-Nagumo equation admits a stable traveling pulse solution for sufficiently small ε>0. In this paper we prove the existence of such a solution for ε=0.01. 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.
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