Web of Science: 5 cites, Scopus: 5 cites, Google Scholar: cites
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))

Data: 2019
Resum: 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 [J. M. Ginoux and J. Llibre, Qual. Theory Dyn. Syst. 15 (2016) 381-431; J. M. Ginoux and J. Llibre, Qual. Theory Dyn. Syst. 15 (2015) 342010]. 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.
Ajuts: Ministerio de Economía y Competitividad MTM2016-77278-P
Ministerio de Economía y Competitividad MTM2013-40998-P
Drets: Tots els drets reservats.
Llengua: Anglès
Document: Article ; recerca ; Versió acceptada per publicar
Matèria: Hindmarsh-Rose model ; Singularly perturbed dynamical systems ; Canard solutions
Publicat a: Mathematical Modelling of Natural Phenomena, Vol. 14, Issue 4 (2019) , art. 409, ISSN 1760-6101

DOI: 10.1051/mmnp/2019012


Postprint
16 p, 706.1 KB

21 p, 529.6 KB

El registre apareix a les col·leccions:
Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
Articles > Articles de recerca
Articles > Articles publicats

 Registre creat el 2020-04-15, darrera modificació el 2023-11-27



   Favorit i Compartir