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 Rus. J. Nonlin. Dyn., 2021, Volume 17, Number 1, Pages 103–117 (Mi nd744)

Mathematical problems of nonlinearity

Peculiarities of Synchronization in a Two-Layer Network of Chaotic Maps with Inhomogeneous Interlayer Coupling

T. R. Bogatenko, A. V. Bukh, G. I. Strelkova

Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia

Abstract: This paper considers the effects of forced and mutual synchronization of complex spatiotemporal structures in a two-layer network of nonlocally coupled logistic maps in the presence of inhomogeneous interlayer coupling. Two different types of coupling topology are considered: the first one is the sparse interlayer coupling with randomly distributed coupling defects, and the second type is the cluster interlayer coupling, providing the coupling via designated finite groups of elements. The latter type of coupling topology is considered for the first time. As a quantitative measure of the synchronization effect on the network, variance averaged over time and variance averaged both over time and network elements are used. We analyze how the synchronization measure changes depending on a degree of the interlayer coupling sparseness. We also identify a cluster of network elements which can provide almost complete synchronization in the network under study when the interlayer coupling is introduced along them.

Keywords: synchronization, sparse links, chimera state, multilayer network, interlayer coupling

 Funding Agency Grant Number Deutsche Forschungsgemeinschaft 163436311-SFB 910 Russian Foundation for Basic Research 20-52-12004 This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — Project number 163436311-SFB 910 and by RFBR and DFG according to the research project No. 20-52-12004.

DOI: https://doi.org/10.20537/nd210108

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MSC: 34H05, 37D99
Accepted:22.03.2021
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Citation: T. R. Bogatenko, A. V. Bukh, G. I. Strelkova, “Peculiarities of Synchronization in a Two-Layer Network of Chaotic Maps with Inhomogeneous Interlayer Coupling”, Rus. J. Nonlin. Dyn., 17:1 (2021), 103–117

Citation in format AMSBIB
\Bibitem{BogBukStr21} \by T. R. Bogatenko, A. V. Bukh, G. I. Strelkova \paper Peculiarities of Synchronization in a Two-Layer Network of Chaotic Maps with Inhomogeneous Interlayer Coupling \jour Rus. J. Nonlin. Dyn. \yr 2021 \vol 17 \issue 1 \pages 103--117 \mathnet{http://mi.mathnet.ru/nd744} \crossref{https://doi.org/10.20537/nd210108} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=4240820} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85105214747}