4.7 Article

Coupled systems with quasi-periodic and chaotic dynamics

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CHAOS SOLITONS & FRACTALS
卷 169, 期 -, 页码 -

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PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2023.113278

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Quasi-periodic oscillations; Dynamical chaos; Ro center dot ssler system; Lyapunov exponents; chaos with additional zero Lyapunov exponents

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The interaction between a system with quasi-periodic autonomous dynamics and a chaotic Rössler system is studied. The coupling growth leads to the emergence of two-frequency and three-frequency quasi-periodicity, periodicity, and oscillation death in sequence. The system exhibits doubling bifurcations of three-frequency tori with small coupling strength. A chaotic regime with two additional zero Lyapunov exponents in the spectrum is discovered. Two-parameter Lyapunov exponent analysis and bifurcation analysis are conducted, and a new bifurcation scenario from oscillation death to quasi-periodicity in coupled systems is described.
The interaction of a system with quasi-periodic autonomous dynamics and a chaotic Ro center dot ssler system is studied. We have shown that with the growth of the coupling, regimes of two-frequency and three-frequency quasipe-riodicity, 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.

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