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Journal Articles Chaos: An Interdisciplinary Journal of Nonlinear Science Year : 2017

Synchronizability of nonidentical weakly dissipative systems

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Abstract

Synchronization is a very generic process commonly observed in a large variety of dynamical systems which, however, has been rarely addressed in systems with low dissipation. Using the R€ ossler, the Lorenz 84, and the Sprott A systems as paradigmatic examples of strongly, weakly, and non-dissipative chaotic systems, respectively, we show that a parameter or frequency mismatch between two coupled such systems does not affect the synchronizability and the underlying structure of the joint attractor in the same way. By computing the Shannon entropy associated with the corresponding recurrence plots, we were able to characterize how two coupled nonidentical chaotic oscillators organize their dynamics in different dissipation regimes. While for strongly dissipative systems, the resulting dynamics exhibits a Shannon entropy value compatible with the one having an average parameter mismatch, for weak dissipation synchronization dynamics corresponds to a more complex behavior with higher values of the Shannon entropy. In comparison, conservative dynamics leads to a less rich picture, providing either similar chaotic dynamics or oversimplified periodic ones. Published by AIP Publishing. https://doi.org/10.1063/1.5005840 Weakly dissipative systems, typically found in celestial mechanics, fluid mechanics, meteorology, mechanics, ecology, etc., have solutions that visit a non-zero volume of the state space in contrast with those being strongly dissipative. As a consequence, the characterization of their chaotic attractor is much more complicated. When synchronization is considered, it is of great interest to consider if strongly or weakly dissipative systems behave similarly or not. Here, we compared, by using the Shannon entropy, the way nonidentical systems presenting different dissipation rates organize into a collective dynamics and found that low dissipation favors an increase of the Shannon entropy of the interacting systems while high dissipation gives rise to a dynamics whose complexity is in between of the coupled ones.
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hal-01672078 , version 1 (23-12-2017)

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Irene Sendina-Nadal, Christophe Letellier. Synchronizability of nonidentical weakly dissipative systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017, 27 (10), ⟨10.1063/1.5005840⟩. ⟨hal-01672078⟩
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