The structure of the quiescent core in rigidly rotating spirals in a class of excitable systems

Maria Aguareles; Marco A. Fontelos; Juan J. Velázquez

doi:10.3934/dcdsb.2012.17.1605

Article Contents

2012, Volume 17, Issue 6: 1605-1638. Doi: 10.3934/dcdsb.2012.17.1605

This issue Previous Article Preface Next Article On the validity of formal asymptotic expansions in Allen-Cahn equation and FitzHugh-Nagumo system with generic initial data

The structure of the quiescent core in rigidly rotating spirals in a class of excitable systems

1.
Departament d'Informàtica i Matemàtica Aplicada. Universitat de Girona, Campus Montilivi, EPS-P4, Girona, 17071
2.
ICMAT (CSIC-UAM-UC3M-UCM), C/Nicolás Cabrera 15, Madrid, 28049
3.
Institute for Applied Mathematics. University of Bonn., Endenicher Allee 60, Bonn, D-53115

Received: April 30, 2011

Revised: July 31, 2011

Published: August 2012

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Abstract

We consider a class of excitable system whose dynamics is described by Fitzhugh-Nagumo (FN) equations. We provide a description for rigidly rotating spirals based on the fact that one of the unknowns develops abrupt jumps in some regions of the space. The core of the spiral is delimited by these regions. The description of the spiral is made using a mixture of asymptotic and rigorous arguments. Several open problems whose rigorous solution would provide insight in the problem are formulated.

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Mathematics Subject Classification: Primary: 35Q92, 35K57; Secondary: 35B25.

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