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Asymptotic multistability and local S-asymptotic ω-periodicity for the nonautonomous fractional-order neural networks with impulses

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Abstract

This paper focuses on the investigation of asymptotic multistability and on local S-asymptotic ω-periodicity for nonautonomous fractional-order neural networks (FONNs) with impulses. Several criteria on the existence, uniqueness, and invariant sets of nonautonomous FONNs with impulses are derived by constructing convergent sequences and comparison principles, respectively. In addition, using the Lyapunov direct method, some novel conditions of boundedness and local asymptotic stability of the FONNs discussed are obtained. Also, the sufficient conditions for local S-asymptotic ω-periodicities of the system are presented. Finally, a discussion using two examples verifies the validity of our findings, which imply that global asymptotic stability is a special case of asymptotic multistability.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61873071) and Shandong Provincial Natural Science Foundation (Grant No. ZR2019MF006).

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, 264209, China

    Yonggui Kao & Hui Li

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  1. Yonggui Kao
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  2. Hui Li
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Correspondence to Yonggui Kao.

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Kao, Y., Li, H. Asymptotic multistability and local S-asymptotic ω-periodicity for the nonautonomous fractional-order neural networks with impulses. Sci. China Inf. Sci. 64, 112207 (2021). https://doi.org/10.1007/s11432-019-2821-x

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  • DOI: https://doi.org/10.1007/s11432-019-2821-x

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