Gianni Arioli, Hans Koch
Existence and stability of traveling pulse solutions
of the FitzHugh-Nagumo equation
(1086K, plain TeX, with eps figures)
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.