Fitzhugh-Nagumo equations in a nonhomogeneous medium

Arnold Dikansky

doi:10.3934/proc.2005.2005.216

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2005, Volume 2005: 216-224. Doi: 10.3934/proc.2005.2005.216 open access

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Fitzhugh-Nagumo equations in a nonhomogeneous medium

Arnold Dikansky^1,

1.
St. John's University, 300 Howard Av., Staten Island, NY 10301

Received: August 31, 2004

Revised: January 31, 2005

Published: August 2005

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Abstract

In this paper we investigate various propagation phenomena for the FitzHugh-Nagumo system (% (4) with a nonhomogeneous threshold function $a(x)$. It is studied over a range of values $b$, $d,\varepsilon $ and function $a(x).$ Numerical simulations of system show that system (\ref{fh}) exhibits different patterns of behavior and they significantly differ from those in a homogeneous medium.

Keywords:

reaction-diffusion,
FitzHugh-Nagumo.

Mathematics Subject Classification: Primary: 35K57, 37N25; Secondary: 47N20.

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