Zero-Hopf bifurcation in a Chua system
D. Euzébio, Rodrigo (Universidade Estadual Paulista (Brasil). Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2017
Abstract:	A zero-Hopf equilibrium is an isolated equilibrium point whose eigenvalues are ±ωi ̸= 0 and 0. In general for a such equilibrium there is no theory for knowing when it bifurcates some small-amplitude limit cycles moving the parameters of the system. Here we study the zero-Hopf bifurcation using the averaging theory. We apply this theory to a Chua system depending on 6 parameters, but the way followed for studying the zero-Hopf bifurcation can be applied to any other di erential system in dimension 3 or higher. In this paper rst we show that there are three 4-parameter families of Chua systems exhibiting a zero-Hopf equilibrium. After, by using the averaging theory, we provide su cient conditions for the bifurcation of limit cycles from these families of zero-Hopf equilibria. From one family we can prove that 1 limit cycle bifurcates, and from the other two families we can prove that 1, 2 or 3 limit cycles bifurcate simultaneously.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999 Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P
Note:	Agraïments: The first author is supported by the FAPESP-BRAZIL grants 2010/18015-6, 2012/05635-1, and 2013/25828-1. The second author is partially supported by FEDER-UNAB-10-4E-378, and a CAPES grant 88881. 030454/2013-01 do Programa CSF-PVE.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Chua system ; Periodic orbit ; Zero-Hopf bifurcation
Published in:	Nonlinear Analysis: Real World Applications, Vol. 37 (2017) , p. 31-40, ISSN 1468-1218

DOI: 10.1016/j.nonrwa.2017.02.002

Postprint 11 p, 698.6 KB

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