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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.
Note: Número d'acord de subvenció MINECO/MTM2013-40998-P
Note: Número d'acord de subvenció AGAUR/2014/SGR-568
Note: Número d'acord de subvenció EC/FP7/2012/316338
Note: Número d'acord de subvenció EC/FP7/2012/318999
Rights: Tots els drets reservats.
Language: Anglès.
Document: article ; recerca ; submittedVersion
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 0218-1274 (Print)

DOI: 10.1142/S0218127417500687


Preprint
9 p, 288.4 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2017-11-28, last modified 2019-02-02



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