Home > Books and collections > Book chapters > Canards existence in the Hindmarsh-Rose model |
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 |
Post-print 5 p, 251.1 KB |