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A threshold effect of coupling delays on intra-layer synchronization in duplex networks

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Abstract

This paper investigates the impact of inter-layer coupling functions and intra-layer coupling delays on intra-layer synchronization regions and sychronizability. It is found that the inter-layer coupling functions have great influence on intra-layer synchronization regions, as well as on the intra-layer synchronizability. In particular, there exists an inter-layer coupling function such that the inter-layer coupling strength neither improves nor weakens the intra-layer synchronizability. Furthermore, no matter which one of three inter-layer coupling functions is chosen, a small intra-layer delay always keeps the intra-layer synchronized regions almost unchanged, implying that the small delay neither enhances nor suppresses the intra-layer synchronizability. At the same time the delay greatly frustrates the synchronizability in each layer when it is greater than some threshold. Our results may have potential applications for interconnected technological networks where communication delays are inevitably present.

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Authors and Affiliations

  1. Fujian Province University Key Laboratory of Computation Science, School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China

    LongKun Tang

  2. Department of Mathematics & Statistics, Georgia State University, Atlanta, 30303, USA

    LongKun Tang

  3. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    JunAn Lu

  4. School of Automation Science and Electrical Engineering, State Key Laboratory of Software Development Environment, and Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China

    JinHu Lü

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  1. LongKun Tang
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  2. JunAn Lu
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  3. JinHu Lü
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Correspondence to JinHu Lü.

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Tang, L., Lu, J. & Lü, J. A threshold effect of coupling delays on intra-layer synchronization in duplex networks. Sci. China Technol. Sci. 61, 1907–1914 (2018). https://doi.org/10.1007/s11431-017-9285-7

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