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 <i>0.001</i> and <i>0.1</i> in typical simulations 
of nerve axons. 
Based on the existence of a (singular) limit at &epsilon;<i>=0</i>, 
it has been shown that the FitzHugh-Nagumo equation admits 
a stable traveling pulse solution for sufficiently small &epsilon;<i>>0</i>. 
In this paper we prove the existence of such a solution for &epsilon;<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.