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Synchronization of discontinuous competitive networks modeled by Filippov singular perturbation system: time-scales dependent settling-time

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Abstract

This paper mainly considers the fixed-time synchronization (FxTS) and fixed-time anti-synchronization (FxTAS) of discontinuous competitive neural networks with time scales (DCNNTS) modeled by singularly perturbed Filippov system. Different from the previous FxTS results on the competitive networks, new fixed-time stability lemmas with economical inequality conditions are given, which have more relaxed conditions. Then, by means of the established fixed-time stability lemmas and differential inclusions theory, the FxTS and FxTAS of the addressed drive-response DCNNTS are investigated by constructing two different Lyapunov functions and via new designed non-chattering controllers. Notably, the FxTAS of competitive networks is discussed for the first time. Moreover, time-scales-dependent settling times have also been obtained, which further show the effects of time scales on the FxTS and the FxTAS of DCNNTS. Finally, examples and numerical simulations help examine the correctness of the main results.

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Acknowledgements

The authors thank the anonymous reviewers for their insightful suggestions which improved this work significantly. This work was jointly supported by the National Natural Science Foundation of China (12001011, 62173139), the Natural Science Fund Project of the University in Anhui Province (2022AH030023) and the Science and Technology Innovation Program of Hunan Province (2021RC4030).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241000, Anhui, China

    Fanchao Kong

  2. MOE-LCSM, CHP-LCOCS, School of Mathematical Sciences and Statistics, Hunan Normal University, Changsha, 410081, China

    Fanchao Kong & Quanxin Zhu

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  1. Fanchao Kong
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  2. Quanxin Zhu
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Correspondence to Quanxin Zhu.

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Kong, F., Zhu, Q. Synchronization of discontinuous competitive networks modeled by Filippov singular perturbation system: time-scales dependent settling-time. Nonlinear Dyn 111, 11087–11103 (2023). https://doi.org/10.1007/s11071-023-08422-w

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