Zero-Hopf bifurcations in three-dimensional chaotic systems with one stable equilibrium
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Messias, Marcelo (Universidade Estadual Paulista. Departamento de Matemática e Computação (Brazil))
De Carvalho Reinol, Alisson (Universidade Tecnológica Federal Do Paraná. Departamento Acadêmico de Matemática (Brazil))

Date:	2020
Abstract:	In (Molaie et al. , Int J Bifurcat Chaos 23 (2013) 1350188) the authors provided the expressions of twenty three quadratic differential systems in R3 with the unusual feature of having chaotic dynamics coexisting with one stable equilibrium point. In this paper we consider twenty three classes of quadratic differential systems in R3 depending on a real parameter a which, for a = 1, coincide with the differential systems given by Molaie et al. We study the dynamics and bifurcations of these classes of differential systems by varying the parameter value a. We prove that, for a = 0 all the twenty three considered systems have a zero-Hopf equilibrium point located at the origin. For a > 0 small enough, three periodic orbits bifurcate from the origin: one of them unstable and the other two forming a pair of saddle type periodic orbits. Furthermore, we show numerically that the hidden chaotic attractors which exist for these systems when a = 1 (already described by Molaie et al. ) are obtained by period-doubling route to chaos.
Grants:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Zero-Hopf bifurcation ; Periodic orbits ; Period-doubling route to chaos ; Hidden chaotic attractors
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 30, Issue 13 (October 2020) , art. 2050189, ISSN 1793-6551

DOI: 10.1142/S0218127420501898

Postprint 15 p, 743.5 KB

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