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

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  • Carlos F. da Silva

    (Universidade do Estado de Santa Catarina)

  • Paulo C. Rech

    (Universidade do Estado de Santa Catarina)

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. Graphic abstract

Suggested Citation

  • Carlos F. da Silva & Paulo C. Rech, 2023. "Chaos suppression, hyperchaos, period-adding, and discontinuous spirals in a bidirectional coupling of Lorenz systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(1), pages 1-7, January.
    • Handle: RePEc:spr:eurphb:v:96:y:2023:i:1:d:10.1140_epjb_s10051-022-00476-w
    DOI: 10.1140/epjb/s10051-022-00476-w
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    Cited by:

    1. 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.
    2. Maranhão, Dariel M. & Medrano-T, Rene O., 2024. "Periodicity in the asymmetrical quartic map," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).

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