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Coupled systems with quasi-periodic and chaotic dynamics

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  • Kuznetsov, Alexander P.
  • Sedova, Yuliya V.
  • Stankevich, Nataliya V.

Abstract

The interaction of a system with quasi-periodic autonomous dynamics and a chaotic Rössler system is studied. We have shown that with the growth of the coupling, regimes of two-frequency and three-frequency quasiperiodicity, a periodic regime and a regime of oscillation death sequentially arise. With a small coupling strength, doubling bifurcations of three-frequency tori are observed in the system. A chaotic regime, characterized by two additional zero Lyapunov exponents in spectrum, is revealed. Two-parameter Lyapunov exponent analysis and bifurcation analysis are presented. A new bifurcation scenario of transition from the regime of oscillation death to quasi-periodicity in coupled systems is described.

Suggested Citation

  • Kuznetsov, Alexander P. & Sedova, Yuliya V. & Stankevich, Nataliya V., 2023. "Coupled systems with quasi-periodic and chaotic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001790
    DOI: 10.1016/j.chaos.2023.113278
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    1. Zhusubaliyev, Zhanybai T. & Avrutin, Viktor & Medvedev, Alexander, 2021. "Doubling of a closed invariant curve in an impulsive Goodwin’s oscillator with delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
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    Cited by:

    1. Molaie, Moslem & Samani, Farhad S. & Zippo, Antonio & Iarriccio, Giovanni & Pellicano, Francesco, 2023. "Spiral bevel gears: Bifurcation and chaos analyses of pure torsional system," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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