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Excitable chaos in diffusively coupled FitzHugh-Nagumo equations

 

G. Baier and M. Müller

 

Facultad de Ciencias, Universidad Autónoma del Estado de Morelos 62210 Cuernavaca, Morelos, México e-mail: baier@servm.fc.uaem.mx.

 

Recibido el 14 de octubre de 2003.
Aceptado el 26 de abril de 2004.

 

Abstract

A prototypic model of three coupled FitzHugh-Nagumo oscillators is shown to exhibit spatio-temporal hyperchaos. With increasing the number of coupled units the number of positive Lyapunov exponents increases. A system in two spatial dimensions shows two types of excitable spatio-temporal (hyper-)chaos depending on which variable is chosen for the coupling. Some implications for excitable cardiac tissue are discussed.

Keywords: FitzHugh-Nagumo equation; hyperchaos; spatio-temporal chaos.

 

Resumen

Un modelo prototípico de tres osciladores acoplados tipo FitzHugh-Nagumo muestra hipercaos espacio-temporal. Aumentando el número de unidades acopladas se aumenta el número de exponentes de Lyapunov positivos. Un sistema extendido en dos dimensiones espaciales genera dos tipos de (hiper-)caos excitable espacio-temporal dependiente de la variable de acoplamiento. Se discuten unas implicaciones para tejidos excitables cardiacos.

Descriptores: Ecuación de FitzHugh-Nagumo; hipercaos; caos espacio-temporal.

 

PACS: 05.45.-a; 05.45.Pq; 87.17.Hf

 

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Acknowledgments

Work was supported by CONACyT, Mexico (project no. 40885-F). G.B. thanks Sven Sahle for help with finding the supercritical Hopf condition and for discussion during an early stage of the present work.

 

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