Abstract:Background and Objectives: Effects of mutual and external synchronization of chimera states are studied in two coupled ensembles of discrete maps. Each of the ensembles is a onedimensional ring of nonlocally coupled cubic maps in the chaotic oscillation mode. In order to create differences in the dynamics of the ensembles when there is no coupling between them, a mismatch is introduced in the parameters of the individual oscillators of the first and second rings. Effects of external and mutual synchronization of chimera states are explored in detail. Materials and Methods: The effect of synchronization of spatio-temporal structures in two coupled ensembles of discrete nonlinear oscillators is studied numerically. The identity of synchronous structures and synchronization regions was quantified by of calculating the cross-correlation coefficient between the corresponding oscillators of interconnected ensembles. Results: The effects of mutual and external synchronization of chimera structures have been established and confirmed by snapshots of the amplitude of oscillations, by calculations of the cross-correlation coefficient between the respective elements of the ensembles and by plotting the synchronization regions on the coupling parameter. Conclusions: The paper presents the numerical results which show that the realization of the effects of mutual and external synchronization of chimera states can be realized in two nonlocally coupled ensembles of cubic maps. The identity of synchronous chimera states and the presence of a finite region of synchronization in the variation of the coupling coefficient between the interacting ensembles are confirmed.
This work was supported by the Ministry of Education and Science of the Russian Federation (project no. 3.8616.2017/8.9).
Document Type:
Article
UDC:
537.86:530.182
Language: Russian
Citation:
I. А. Kholuianova, S. A. Bogomolov, V. S. Anishchenko, “Synchronization of chimera states in ensembles of nonlocally coupled cubic maps”, Izv. Sarat. Univ. Physics, 18:2 (2018), 103–111
\Bibitem{KhoBogAni18}
\by I.~А.~Kholuianova, S.~A.~Bogomolov, V.~S.~Anishchenko
\paper Synchronization of chimera states in ensembles of nonlocally coupled cubic maps
\jour Izv. Sarat. Univ. Physics
\yr 2018
\vol 18
\issue 2
\pages 103--111
\mathnet{http://mi.mathnet.ru/isuph312}
\crossref{https://doi.org/10.18500/1817-3020-2018-18-2-103-111}
Linking options:
https://www.mathnet.ru/eng/isuph312
https://www.mathnet.ru/eng/isuph/v18/i2/p103
This publication is cited in the following 2 articles:
S. A. Bogomolov, E. V. Rybalova, G. I. Strelkova, V. S. Anischenko, “Prostranstvenno-vremennye struktury v ansamble nelokalno svyazannykh otobrazhenii Nekorkina”, Izv. Sarat. un-ta. Nov. cer. Ser. Fizika, 19:2 (2019), 86–94
V. I. Ponomarenko, D. D. Kulminskii, E. I. Borovkova, M. D. Prokhorov, “Upravlenie kollektivnoi dinamikoi v seti bistabilnykh sistem s zapazdyvaniem, svyazannykh cherez obschee pole”, Izv. Sarat. un-ta. Nov. cer. Ser. Fizika, 19:4 (2019), 258–269
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