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On the dynamics of a Van der Pol–Duffing snap system

Author

Listed:
  • Vinícius Wiggers

    (Universidade do Estado de Santa Catarina)

  • Paulo C. Rech

    (Universidade do Estado de Santa Catarina)

Abstract

In this paper, we propose an autonomous snap oscillator which was obtained from the Van der Pol–Duffing forced oscillator. The proposed system presents polynomial nonlinearities, being modeled by a four-parameter fourth-order ordinary differential equation. We investigate the dynamics of this system. More specifically, keeping two of the parameters fixed, we investigate numerically the organization of chaos and periodicity in this system, using an appropriately chosen parameter plane. We show that such parameter plane presents parameters regions for which the multistability phenomenon is perfectly characterized. Plots of basins of attraction and coexisting attractors are presented. An analytical investigation regarding the stability of equilibrium points was also carried out. Graphic abstract

Suggested Citation

  • Vinícius Wiggers & Paulo C. Rech, 2022. "On the dynamics of a Van der Pol–Duffing snap system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(2), pages 1-6, February.
    • Handle: RePEc:spr:eurphb:v:95:y:2022:i:2:d:10.1140_epjb_s10051-022-00294-0
    DOI: 10.1140/epjb/s10051-022-00294-0
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    Citations

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    Cited by:

    1. Isabelle L. Soares & Marcelo F. Krol & Paulo C. Rech, 2024. "Coexisting attractors and basins of attraction of an extended forced Duffing oscillator," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-6, June.
    2. N. C. Pati, 2023. "Bifurcations and multistability in a physically extended Lorenz system for rotating convection," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-15, August.

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