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Distributed Pinning Impulsive Control for Inner–Outer Synchronization of Dynamical Networks on Time Scales

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Abstract

In this paper, inner–outer synchronization problem of dynamical networks on time scales is studied. This kind of network synchronization means that two dynamical networks can achieve inner/outer synchronization simultaneously. By designing suitable distributed pinning impulsive controllers, the inner–outer synchronization target is realized. Based on the Lyapunov function method and the mathematical induction approach, two sufficient criteria are given for inner–outer synchronization of two networks with identical and non-identical topologies. Due to the structure of time scales, the derived results can be applied to study the inner–outer synchronization problems of continuous/discrete networks and networks on hybrid time domains. A numerical simulation example is given to illustrate the effectiveness of the derived results.

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Acknowledgements

This work is supported by by the National Natural Science Foundation of China under Grants 61873150, 61503225 the Natural Science Fund for Distinguished Young Scholars of Shandong Province under Grant JQ201613.

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  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People’s Republic of China

    Xiaodong Lu & Haitao Li

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  1. Xiaodong Lu
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  2. Haitao Li
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Correspondence to Xiaodong Lu.

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The authors declare that they have no conflict of interest to this work. There is no professional or other personal interest of any nature or kind in any product that could be construed as influencing the position presented in the manuscript entitled.

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Lu, X., Li, H. Distributed Pinning Impulsive Control for Inner–Outer Synchronization of Dynamical Networks on Time Scales. Neural Process Lett 51, 2481–2495 (2020). https://doi.org/10.1007/s11063-020-10204-z

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