Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation

Keywords

Advanced Numerical Methods for Scientific Computing
Code:
62/2013
Title:
Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation
Date:
Sunday 1st December 2013
Author(s):
Arioli, G.; Koch, H.
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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 epsilon 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 epsilon = 0, it has been shown that the FitzHugh-Nagumo equation admits a stable traveling pulse solution for sufficiently small epsilon > 0. In this paper we prove the existence of such a solution for epsilon = 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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