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Chaos suppression, hyperchaos, period-adding, and discontinuous spirals in a bidirectional coupling of Lorenz systems

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Abstract

In this paper we report on a novel continuous-time autonomous six-dimensional dynamical system, obtained by coupling two Lorenz systems. The parameter plane involving the parameters present in the coupling function is investigated. We consider two cases, namely (i) a coupling of two identical chaotic Lorenz systems, and (ii) a coupling of two Lorenz systems, one chaotic and the other periodic. In the (i) case, we show that the bidirectional coupling is responsible for the occurrence of chaotic suppression, characterized by the presence of quasiperiodic regions in the parameter plane of the coupled system. Hyperchaos is also observed, as a consequence of the coupling. In the (ii) case, we show that quasiperiodicity is not observed, while hyperchaos occurs in a very small region of the parameter plane. We also show that the investigated parameter plane displays organized periodic structures embedded in a chaotic region. Period-adding sequences and discontinuous spirals are the types of such organizations that have been observed.

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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

    Carlos F. da Silva & Paulo C. Rech

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  1. Carlos F. da Silva
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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.

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Correspondence to Paulo C. Rech.

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Silva, C.F.d., Rech, P.C. Chaos suppression, hyperchaos, period-adding, and discontinuous spirals in a bidirectional coupling of Lorenz systems. Eur. Phys. J. B 96, 4 (2023). https://doi.org/10.1140/epjb/s10051-022-00476-w

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