Zero-Hopf bifurcation in the Fitzhugh-Nagumo system
D. Euzébio, Rodrigo (UNESP(Brazil). Departament de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Vidal, Claudio (Universidad del Bio Bio(Chile). Departamento de Matemática)

Date:	2014
Abstract:	We characterize the values of the parameters for which a zero-Hopf equilibrium point takes place at the singular points, namely, O (the origin), P+ and P− in the FitzHugh-Nagumo system. Thus we find two 2-parameter families of the FitzHugh-Nagumo system for which the equilibrium point at the origin is a zero-Hopf equilibrium. For these two families we prove the existence of a periodic orbit bifurcating from the zero-Hopf equilibrium point O. We prove that exist three 2-parameter families of the FitzHughNagumo system for which the equilibrium point at P+ and P− is a zero-Hopf equilibrium point. For one of these families we prove the existence of 1, or 2, or 3 periodic orbits borning at P+ and P−.
Grants:	Ministerio de Ciencia e Innovación MTM 2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338
Note:	Agraïments: The first author is supported by the FAPESP-BRAZIL grants 2010/18015-6 and 2012/05635-1. The third author is partially supported by Dirección de Investigación DIUBB 120408 4/R.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	FitzHugh-Nagumo system ; Periodic orbit ; Averaging theory ; Zero Hopf bifurcation
Published in:	Mathematical methods in the applied sciences, 2014 , ISSN 1099-1476

DOI: 10.1002/mma.3365

Postprint 15 p, 712.5 KB

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