School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China.
School of Computer Science and Technology, Jiangsu Normal University, Xuzhou, 221116, China.
Neural Netw. 2023 May;162:175-185. doi: 10.1016/j.neunet.2023.02.030. Epub 2023 Mar 2.
This paper studies the global Mittag-Leffler (M-L) stability problem for fractional-order quaternion-valued memristive neural networks (FQVMNNs) with generalized piecewise constant argument (GPCA). First, a novel lemma is established, which is used to investigate the dynamic behaviors of quaternion-valued memristive neural networks (QVMNNs). Second, by using the theories of differential inclusion, set-valued mapping, and Banach fixed point, several sufficient criteria are derived to ensure the existence and uniqueness (EU) of the solution and equilibrium point for the associated systems. Then, by constructing Lyapunov functions and employing some inequality techniques, a set of criteria are proposed to ensure the global M-L stability of the considered systems. The obtained results in this paper not only extends previous works, but also provides new algebraic criteria with a larger feasible range. Finally, two numerical examples are introduced to illustrate the effectiveness of the obtained results.
本文研究了具有广义分段常变量（GPCA）的分数阶四元数值忆阻神经网络（FQVMNNs）的全局 Mittag-Leffler（M-L）稳定性问题。首先，建立了一个新的引理，用于研究四元数值忆阻神经网络（QVMNNs）的动态行为。其次，利用微分包含、集值映射和巴拿赫不动点理论，导出了几个充分条件，以确保相关系统解和平衡点的存在唯一性（EU）。然后，通过构造李雅普诺夫函数并运用一些不等式技术，提出了一组准则来确保所考虑系统的全局 M-L 稳定性。本文得到的结果不仅扩展了以前的工作，而且提供了具有更大可行范围的新的代数准则。最后，介绍了两个数值实例来说明所得到结果的有效性。
