Zhang Fanghai, Zeng Zhigang
IEEE Trans Neural Netw Learn Syst. 2022 Sep;33(9):4515-4526. doi: 10.1109/TNNLS.2021.3057861. Epub 2022 Aug 31.
This article investigates the multistability and stabilization of fractional-order competitive neural networks (FOCNNs) with unbounded time-varying delays. By utilizing the monotone operator, several sufficient conditions of the coexistence of equilibrium points (EPs) are obtained for FOCNNs with concave-convex activation functions. And then, the multiple μ -stability of delayed FOCNNs is derived by the analytical method. Meanwhile, several comparisons with existing work are shown, which implies that the derived results cover the inverse-power stability and Mittag-Leffler stability as special cases. Moreover, the criteria on the stabilization of FOCNNs with uncertainty are established by designing a controller. Compared with the results of fractional-order neural networks, the obtained results in this article enrich and improve the previous results. Finally, three numerical examples are provided to show the effectiveness of the presented results.
本文研究了具有无界时变延迟的分数阶竞争神经网络（FOCNNs）的多重稳定性和镇定问题。通过利用单调算子，对于具有凹凸激活函数的FOCNNs，获得了平衡点共存的几个充分条件。然后，通过解析方法推导了时滞FOCNNs的多重μ稳定性。同时，给出了与现有工作的若干比较，这意味着所推导的结果涵盖了作为特殊情况的逆幂稳定性和米塔格 - 莱夫勒稳定性。此外，通过设计控制器建立了具有不确定性的FOCNNs的镇定准则。与分数阶神经网络的结果相比，本文得到的结果丰富和改进了先前的结果。最后，提供了三个数值例子以说明所提出结果的有效性。
