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SCIENCE CHINA Information Sciences, Volume 64 , Issue 1 : 112207(2021) https://doi.org/10.1007/s11432-019-2821-x

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

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  • ReceivedAug 2, 2019
  • AcceptedDec 2, 2019
  • PublishedDec 24, 2020

Abstract

This paper focuses on the investigation of asymptotic multistability and on local S-asymptotic $\omega$-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 $\omega$-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.


Acknowledgment

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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