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Blowout bifurcation and chaos-hyperchaos transition in five-dimensional continuous autonomous systems. (English) Zbl 1197.37068

Summary: Blowout bifurcation in chaotic systems occurs when a chaotic attractor lying in some symmetric subspace, becomes transversely unstable. There has been previous reports of chaos-hyperchaos transition via blowout bifurcation in synchronization of identical chaotic systems. In this paper, two five-dimensional continuous autonomous systems are considered, in which a two-dimensional subsystem is driven by a chaotic system. As a system parameter changes, blowout bifurcations occur in these systems and bring on changes of the systems’ dynamics. It is observed that one system undergoes a symmetric hyperchaos-chaos-hyperchaos transition via blowout bifurcations, while the other system does not transit to hyperchaos after the bifurcations. We investigate the dynamical behaviours before and after the blowout bifurcation in the systems and make an analysis of the transition process. It is shown that in such coupled chaotic continuous systems, blowout bifurcation may indicate a transition from chaos to hyperchaos for the whole systems, which provides a possible route to hyperchaos.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:

37G99 Local and nonlocal bifurcation theory for dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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