Degenerate Fold-Hopf Bifurcations in a Rössler-Type System
Tigan, Gheorghe (Politehnica University of Timisoara (Romania). Department of Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Ciurdariu, Loredana (Politehnica University of Timisoara (Romania). Department of Mathematics)

Date:	2017
Abstract:	We study the Hopf and the fold--Hopf bifurcations of the R\"ossler--type differential system * =-y-z, =x ay, =-cz byz, * with b 0. We show that the classical Hopf bifurcation cannot be applied to this system for detecting the fold--Hopf bifurcation, which here is studied using the averaging theory. Our results show that a Hopf bifurcation takes place at the equilibrium (-ac/b,c/b,-c/b) when c=a<0. This Hopf bifurcation becomes a fold--Hopf bifurcation when c=a=0.
Grants:	Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Fold-Hopf bifurcation ; Periodic orbit ; Rössler system ; Zero-Hopf bifurcation
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 27 Núm. 5 (2017) , p. 1750068, ISSN 1793-6551

DOI: 10.1142/S0218127417500687

Postprint 9 p, 288.4 KB

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