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Periodicity suppression and period-adding caused by a parametric excitation in the Lorenz system

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Abstract

In this paper, we propose a continuous-time nonautonomous three-dimensional dynamical system, which was obtained from the original Lorenz system by introducing a parametric sinusoidal excitation. We show that, depending on the magnitude of the angular frequency of the sinusoidal excitation, two independent phenomena may occur: (i) the complete suppression of the periodic structures embedded in the chaotic region of the \((r,\sigma )\) parameter plane of the original Lorenz system, resulting in a chaos region completely free from periodic windows, and (ii) the appearance of other periodic structures, this time organized in period-adding sequences, embedded in the chaotic region of this same parameter plane.

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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 author thanks 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

    Paulo C. Rech

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  1. Paulo C. Rech
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This work was carried out by the author. The author performed the computations. The author wrote this version of the manuscript.

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Correspondence to Paulo C. Rech.

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Rech, P.C. Periodicity suppression and period-adding caused by a parametric excitation in the Lorenz system. Eur. Phys. J. B 95, 169 (2022). https://doi.org/10.1140/epjb/s10051-022-00432-8

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  • DOI: https://doi.org/10.1140/epjb/s10051-022-00432-8

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