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A New Lyapunov Function Method to the Fixed-Time Cluster Synchronization of Directed Community Networks

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Abstract

In this paper, the issue of fixed-time cluster synchronization is investigated for the directed community networks. We propose a new Lyapunov function method which leads to the settling time is not only independent of the initial value, but also unrelated to the number and dimensions of nodes in the networks. This means our estimated settling time is more accurate and much tighter than the one in the existing results. By designing the corresponding controllers and using the fixed-time stability theorem, some new criteria are derived to guarantee that the community networks achieve cluster synchronization in fixed time. Finally, an illustrative example with computer simulations is given to verify the theoretical analysis.

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Acknowledgements

This work was jointly supported by the National Natural Science Foundation of China under Grant No. 61673111, the National Key Research and Development Program of China under Grant No. 2018AAA0100202, and the Fundamental Research Funds for the Central Universities under Grant No. 2242021k10007.

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Authors and Affiliations

  1. The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of Mathematics, Southeast University, Nanjing, 211189, China

    Feilong Zhou & Xiaobing Nie

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  1. Feilong Zhou
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  2. Xiaobing Nie
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Correspondence to Xiaobing Nie.

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Zhou, F., Nie, X. A New Lyapunov Function Method to the Fixed-Time Cluster Synchronization of Directed Community Networks. Neural Process Lett 54, 2143–2164 (2022). https://doi.org/10.1007/s11063-021-10723-3

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