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Chaos of the Rayleigh–Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation

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  • Zhou, Liangqiang
  • Chen, Fangqi

Abstract

With both analytical and numerical methods, chaotic motions of the Rayleigh–Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation are investigated in this paper. Chaos arising from homoclinic or heteroclinic intersections is studied with the Melnikov method. Chaos threshold is obtained and chaotic feature on the system parameters is investigated in detail. Some new interesting dynamic phenomena including “controllable frequency interval”, “chaotic band” and “uncontrollable parameters” are presented and proved rigorously. Numerical simulations are given to verify chaos threshold obtained by the analytical results.

Suggested Citation

  • Zhou, Liangqiang & Chen, Fangqi, 2022. "Chaos of the Rayleigh–Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 1-18.
    • Handle: RePEc:eee:matcom:v:192:y:2022:i:c:p:1-18
    DOI: 10.1016/j.matcom.2021.08.014
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    References listed on IDEAS

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    1. Siewe, M. Siewe & Cao, Hongjun & Sanjuán, Miguel A.F., 2009. "Effect of nonlinear dissipation on the basin boundaries of a driven two-well Rayleigh–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1092-1099.
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    Cited by:

    1. Zhang, Yufeng & Li, Jing & Zhu, Shaotao & Ma, Zerui, 2024. "Harmonic resonance and bifurcation of fractional Rayleigh oscillator with distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 281-297.
    2. Danjin Zhang & Youhua Qian, 2021. "Fast-Slow Coupling Dynamics Behavior of the van der Pol-Rayleigh System," Mathematics, MDPI, vol. 9(23), pages 1-13, November.
    3. He, Ji-Huan & Jiao, Man-Li & Gepreel, Khaled A. & Khan, Yasir, 2023. "Homotopy perturbation method for strongly nonlinear oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 243-258.

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