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Multistability, period-adding, and spirals in a snap system with exponential nonlinearity

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Abstract

In this paper we investigate analytically and numerically a snap system which has a single nonlinearity of exponential type. The system under investigation is modeled by a three parameter fourth-order autonomous nonlinear ordinary differential equation. By keeping one of these three parameters fixed, we investigate numerically the organization of chaos and periodicity in three parameter planes that consider, each of them, the simultaneous variation of the other two parameters. We show that these parameter planes display self-organized periodic structures embedded in a chaotic region. We also show that these parameter planes present regions for which the multistability phenomenon is perfectly characterized. Plots of basins of attraction and coexisting attractors are presented. Furthermore, an analytical investigation regarding the divergence of the flow and the stability analysis of the related 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 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

    Bruna B. T. Francisco & Paulo C. Rech

Authors
  1. Bruna B. T. Francisco
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  2. Paulo C. Rech
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Contributions

This work was carried out in collaboration between both authors. Both authors 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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Francisco, B.B.T., Rech, P.C. Multistability, period-adding, and spirals in a snap system with exponential nonlinearity. Eur. Phys. J. B 96, 63 (2023). https://doi.org/10.1140/epjb/s10051-023-00536-9

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