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From chaos to quasi-periodicity

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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.

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Authors and Affiliations

  1. Saratov Branch, Kotel’nikov Institute of Radio Engineering and Electronics of RAS, ul. Zelenaya 38, Saratov, 410019, Russia

    Alexander P. Kuznetsov, Igor R. Sataev, Yuliya V. Sedova & Ludmila V. Turukina

  2. Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia

    Alexander P. Kuznetsov, Natalia A. Migunova & Ludmila V. Turukina

Authors
  1. Alexander P. Kuznetsov
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  2. Natalia A. Migunova
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  3. Igor R. Sataev
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  4. Yuliya V. Sedova
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  5. Ludmila V. Turukina
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Correspondence to Alexander P. Kuznetsov.

Additional information

This is a translation of the paper by A.P. Kuznetsov, N.A. Migunova, I.R. Sataev, Yu.V. Sedova, and L.V. Turukina “Dynamics of Coupled Chaotic Oscillators: from Chaos to Quasiperiodicity”, Nelin. Dinam., 2014, vol. 10, no. 4, pp. 387–405, which was published previously only in the Russian language.

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Kuznetsov, A.P., Migunova, N.A., Sataev, I.R. et al. From chaos to quasi-periodicity. Regul. Chaot. Dyn. 20, 189–204 (2015). https://doi.org/10.1134/S1560354715020070

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  • DOI: https://doi.org/10.1134/S1560354715020070

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