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
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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 <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.

Files: 13-91.src( 13-91.comments , 13-91.keywords , fhn5.tex , homoclinic.eps , wave.eps , Section_6.tgz.mm )