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

We consider a class of excitable system whose dynamics is de- scribed 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 delim- ited 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.

The authors were supported by the Catalan and Spanish Government grants 2009SGR345, MTM2008-06349-C03-01, MTM2011-27739-C04-03, MTM2008-03255 and MTM2010-16467

© Discrete and continuous dynamical systems. Series B, 2012, vol. 17, núm. 6, p. 1605-1638

American Institute of Mathematical Sciences

Author: Aguareles Carrero, Maria
Fontelos, Marco A.
Velázquez, Juan J.
Date: 2012 September
Abstract: We consider a class of excitable system whose dynamics is de- scribed 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 delim- ited 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.
The authors were supported by the Catalan and Spanish Government grants 2009SGR345, MTM2008-06349-C03-01, MTM2011-27739-C04-03, MTM2008-03255 and MTM2010-16467
Format: application/pdf
ISSN: 1531-3492 (versió paper)
1553-524X (versió electrònica)
Document access: http://hdl.handle.net/10256/11254
Language: eng
Publisher: American Institute of Mathematical Sciences
Collection: MICINN/PN 2012-2015/MTM2011-27739-C04-03
AGAUR/2014-2016/2014 SGR-345
Reproducció digital del document publicat a: http://dx.doi.org/10.3934/dcdsb.2012.17.1605
Articles publicats (D-IMA)
Is part of: © Discrete and continuous dynamical systems. Series B, 2012, vol. 17, núm. 6, p. 1605-1638
Rights: Tots els drets reservats
Subject: Equacions de reacció-difusió
Reaction-diffusion equations
Equacions diferencials parabòliques
Differential equations, Parabolic
Title: The structure of the quiescent core in rigidly rotating spirals in a class of excitable systems
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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