https://doi.org/10.1140/epjb/s10051-022-00476-w
Regular Article - Statistical and Nonlinear Physics
Chaos suppression, hyperchaos, period-adding, and discontinuous spirals in a bidirectional coupling of Lorenz systems
Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710, Joinville, Brazil
Received:
30
November
2022
Accepted:
19
December
2022
Published online:
10
January
2023
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.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
