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Blowout bifurcation and chaos–hyperchaos transition in five-dimensional continuous autonomous systems

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  • Zhou, Qian
  • Chen, Zeng-qiang
  • Yuan, Zhu-zhi

Abstract

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.

Suggested Citation

  • Zhou, Qian & Chen, Zeng-qiang & Yuan, Zhu-zhi, 2009. "Blowout bifurcation and chaos–hyperchaos transition in five-dimensional continuous autonomous systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 1012-1020.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:1012-1020
    DOI: 10.1016/j.chaos.2007.08.091
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    References listed on IDEAS

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    1. Zhou, Q. & Chen, Z.Q. & Yuan, Z.Z., 2007. "On–off intermittency in continuum systems driven by Lorenz system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 276-290.
    2. Stouboulos, I.N. & Miliou, A.N. & Valaristos, A.P. & Kyprianidis, I.M. & Anagnostopoulos, A.N., 2007. "Crisis induced intermittency in a fourth-order autonomous electric circuit," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1256-1262.
    3. Mahmoud, Gamal M. & Aly, Shaban A. & Farghaly, Ahmed A., 2007. "On chaos synchronization of a complex two coupled dynamos system," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 178-187.
    4. Nikolov, Svetoslav & Clodong, Sébastien, 2006. "Hyperchaos–chaos–hyperchaos transition in modified Rössler systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 252-263.
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