Xiao Jianying, Cao Jinde, Cheng Jun, Wen Shiping, Zhang Ruimei, Zhong Shouming
IEEE Trans Neural Netw Learn Syst. 2021 Aug;32(8):3700-3709. doi: 10.1109/TNNLS.2020.3015952. Epub 2021 Aug 3.
This article is concerned with the problem of the global Mittag-Leffler synchronization and stability for fractional-order quaternion-valued neural networks (FOQVNNs). The systems of FOQVNNs, which contain either general activation functions or linear threshold ones, are successfully established. Meanwhile, two distinct methods, such as separation and nonseparation, have been employed to solve the transformation of the studied systems of FOQVNNs, which dissatisfy the commutativity of quaternion multiplication. Moreover, two novel inequalities are deduced based on the general parameters. Compared with the existing inequalities, the new inequalities have their unique superiorities because they can make full use of the additional parameters. Due to the Lyapunov theory, two novel Lyapunov-Krasovskii functionals (LKFs) can be easily constructed. The novelty of LKFs comes from a wider range of parameters, which can be involved in the construction of LKFs. Furthermore, mainly based on the new inequalities and LKFs, more multiple and more flexible criteria are efficiently obtained for the discussed problem. Finally, four numerical examples are given to demonstrate the related effectiveness and availability of the derived criteria.
本文关注分数阶四元数神经网络（FOQVNNs）的全局Mittag-Leffler同步和稳定性问题。成功建立了包含一般激活函数或线性阈值激活函数的FOQVNNs系统。同时，采用了两种不同的方法，即分离法和非分离法，来解决所研究的FOQVNNs系统的变换问题，该系统不满足四元数乘法的交换律。此外，基于一般参数推导了两个新的不等式。与现有不等式相比，新不等式具有独特的优势，因为它们可以充分利用额外的参数。基于Lyapunov理论，可以轻松构造两个新的Lyapunov-Krasovskii泛函（LKFs）。LKFs的新颖之处在于其参数范围更广，可用于构建LKFs。此外，主要基于新的不等式和LKFs，针对所讨论的问题有效地获得了更多、更灵活的判据。最后，给出了四个数值例子，以证明所推导判据的相关有效性和实用性。
