Canards existence in FitzHugh-Nagumo and Hodgkin-Huxley neuronal models
Ginoux, Jean-Marc (Université de Toulon(France). Laboratoire LSIS)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Additional title:	Canards existence in R 2+2
Date:	2015
Abstract:	In a previous paper we have proposed a new method for proving the existence of "canard solutions" for three and four-dimensional singularly perturbed systems with only one fast variable. The aim of this work is to extend this method to the case of four-dimensional singularly perturbed systems with two slow and two fast variables. This method enables to state a unique generic condition for the existence of "canard solutions" for such four-dimensional singularly perturbed systems which is based on the stability of folded singularities (pseudo singular points in this case) of the normalized slow dynamics deduced from a well-known property of linear algebra. This unique generic condition is perfectly identical to that provided in previous works. Applications of this method to the famous coupled FitzHugh-Nagumo equations and to the Hodgkin-Huxley model enables to show the existence of "canard solutions" in such systems.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338 Ministerio de Economía y Competitividad FEDER-UNAB10-4E-378
Note:	El títol de la versió pre-print de l'article és: Canards existence in R 2+2
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Canard solutions ; Geometric singular perturbation theory ; Singularly perturbed dynamical systems
Published in:	Mathematical Problems in Engineering, Vol. 2015 art. 342010, p. 17pp., ISSN 1563-5147

DOI: 10.1155/2015/342010

Postprint 38 p, 1.1 MB

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