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Multistability and organization of periodicity in a Van der Pol–Duffing oscillator

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  • Wiggers, Vinícius
  • Rech, Paulo C.

Abstract

We investigate the dynamics of a Van der Pol–Duffing forced oscillator, which is modelled by a five-parameter second order nonautonomous nonlinear ordinary differential equation. Firstly we fix three of these parameters, and investigate the dynamics of this system by varying the other two, namely the amplitude and the angular frequency of the external forcing. We also investigate the existence of different attractors, periodic, quasiperiodic, and chaotic. Finally, we investigate the occurrence of multistability in the considered Van der Pol–Duffing forced oscillator, for some fixed sets of parameters.

Suggested Citation

  • Wiggers, Vinícius & Rech, Paulo C., 2017. "Multistability and organization of periodicity in a Van der Pol–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 632-637.
    • Handle: RePEc:eee:chsofr:v:103:y:2017:i:c:p:632-637
    DOI: 10.1016/j.chaos.2017.07.021
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    References listed on IDEAS

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    1. Fabiola Prants & Paulo Rech, 2014. "Organization of periodic structures in a damped-forced oscillator," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(9), pages 1-4, September.
    2. Paulo Rech, 2013. "Nonlinear dynamics investigation in parameter planes of a periodically forced compound KdV-Burgers equation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(8), pages 1-5, August.
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    Cited by:

    1. Han, Haoming & Zhang, Jing & Liu, Yan, 2023. "Stability analysis of hybrid high-order nonlinear multiple time-delayed coupled systems via aperiodically intermittent control," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Jianbin He & Jianping Cai, 2019. "Design of a New Chaotic System Based on Van Der Pol Oscillator and Its Encryption Application," Mathematics, MDPI, vol. 7(8), pages 1-12, August.
    3. Ye, Weijie, 2020. "Dynamics of a revised neural mass model in the stop-signal task," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. da Silva, Angela & Rech, Paulo C., 2018. "Numerical investigation concerning the dynamics in parameter planes of the Ehrhard–Müller system," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 152-157.
    5. Rao, Xiao-Bo & Zhao, Xu-Ping & Chu, Yan-Dong & Zhang, Jian-Gang & Gao, Jian-She, 2020. "The analysis of mode-locking topology in an SIR epidemic dynamics model with impulsive vaccination control: Infinite cascade of Stern-Brocot sum trees," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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