Canards existence in the Hindmarsh-Rose model
Ginoux, Jean-Marc (Centre National de la Recherche Scientifique (França))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tchizawa, Kiyoyuki (Institute of Administration Engineering Ltd. (Japan))

Imprint:	Cham, etc : Birkhäuser, cop. 2019
Description:	5 pàg.
Abstract:	In two previous papers, we have proposed a new method for proving the existence of "canard solutions" on one hand for three- and four-dimensional singularly perturbed systems with only one fast variable and, on the other hand, for four-dimensional singularly perturbed systems with two fast variables; see [4, 5]. The aim of this work is to extend this method, which improves the classical ones used till now to the case of three-dimensional singularly perturbed systems with two fast variables. This method enables to state a unique generic condition for the existence of "canard solutions" for such three-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. Applications of this method to a famous neuronal bursting model enables to show the existence of "canard solutions" in the Hindmarsh-Rose model.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Ciencia e Innovación MDM-2014-0445 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
Rights:	Tots els drets reservats.
Language:	Anglès
Series:	Trends in mathematics. Research perspectives CRM Barcelona ; 11
Document:	Capítol de llibre ; recerca ; Versió acceptada per publicar
Subject:	Hindmarsh-Rose model ; Singularly perturbed dynamical systems ; Canard solutions
Published in:	Extended abstracts Spring 2018 : singularly perturbed systems, multiscale phenomena and hysteresis: theory and applications, 2019, p. 169-175, ISBN 9783030252618

DOI: 10.1007/978-3-030-25261-8_26

Post-print 5 p, 251.1 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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