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

  • Regular Article - Statistical and Nonlinear Physics
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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.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data sets used during the investigation are available from the authors on reasonable request.]

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Acknowledgements

The authors would like to thank Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq, and Fundação de Amparo à Pesquisa e Inovação do Estado de Santa Catarina-FAPESC, Brazilian Agencies, for financial support.

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Authors and Affiliations

  1. Departamento de Física, Universidade do Estado de Santa Catarina, Joinville, 89219-710, Brazil

    Vinícius Wiggers & Paulo C. Rech

Authors
  1. Vinícius Wiggers
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  2. Paulo C. Rech
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Contributions

This work was carried out in collaboration between both authors. Author VW performed the computations. Results were discussed by both authors. Author PCR wrote the first version of the manuscript. Both authors revised the manuscript and approved this version.

Corresponding author

Correspondence to Paulo C. Rech.

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Wiggers, V., Rech, P.C. On the dynamics of a Van der Pol–Duffing snap system. Eur. Phys. J. B 95, 28 (2022). https://doi.org/10.1140/epjb/s10051-022-00294-0

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  • DOI: https://doi.org/10.1140/epjb/s10051-022-00294-0

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