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.

本文着重研究渐近多重稳定性以及带脉冲的非自治分数阶神经网络（FONN）的局部S渐近ω-周期。通过构造收敛序列和比较原理，分别推导了关于非自治带脉冲非神经网络的存在，唯一性和不变集的若干判据。此外，使用Lyapunov直接方法，获得了所讨论的FONN的有界性和局部渐近稳定性的一些新条件。而且，局部S渐近ω的充分条件给出了系统的周期。最后，使用两个示例进行的讨论验证了我们的发现的正确性，这表明全局渐近稳定性是渐近多重稳定性的特例。