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Regular and Chaotic Dynamics

, Volume 20, Issue 2, pp 189–204 | Cite as

From chaos to quasi-periodicity

  • Alexander P. KuznetsovEmail author
  • Natalia A. Migunova
  • Igor R. Sataev
  • Yuliya V. Sedova
  • Ludmila V. Turukina
Article

Abstract

Ensembles of several Rössler chaotic oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of different and sufficiently high dimensional invariant tori. The possibility of a quasi-periodic Hopf bifurcation and a cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonance tori are revealed. Boundaries of these domains correspond to the saddle-node bifurcations. Inside the domains of resonance modes, torus-doubling bifurcations and destruction of tori are observed.

Keywords

chaos quasi-periodic oscillation invariant torus Lyapunov exponent bifurcation 

MSC2010 numbers

70K43 65P20 65P30 34D08 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  • Alexander P. Kuznetsov
    • 1
    • 2
    Email author
  • Natalia A. Migunova
    • 2
  • Igor R. Sataev
    • 1
  • Yuliya V. Sedova
    • 1
  • Ludmila V. Turukina
    • 1
    • 2
  1. 1.Saratov BranchKotel’nikov Institute of Radio Engineering and Electronics of RASSaratovRussia
  2. 2.Saratov State UniversitySaratovRussia

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