Periodic orbits in the zero-Hopf bifurcation of the Rössler system
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2014
Abstract:	A zero-Hopf equilibrium is an isolated equilibrium point whose eigenvalues are ±ωi ̸= 0 and 0. For a such equilibrium there is no a general theory for knowing when from this equilibrium bifurcates a small-amplitude periodic orbit moving the parameters of the system. We provide here an algorithm for solving this problem. In particular, first we characterize the values of the parameters for which a zero-Hopf equilibrium point takes place in the Rössler systems, and we find two one-parameter families exhibiting such equilibria. After for one of these families we prove the existence of one periodic orbit bifurcating from the zero-Hopf equilibrium. The algorithm developed for studying the zero-Hopf bifurcation of the Rössler systems can be applied to other differential system in Rn.
Grants:	European Commission 318999 European Commission 316338 Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Note:	graïments/Ajudes: The second author is partially supported by Fondecyt project 1130644.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Periodic orbit ; Rössler system ; Zero-Hopf bifurcation
Published in:	Romanian Astronomical Journal, Vol. 24 Núm. 1 (2014) , p. 49-60, ISSN 2285-3758

Postprint 11 p, 679.7 KB

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