Novel Inequalities to Global Mittag-Leffler Synchronization and Stability Analysis of Fractional-Order Quaternion-Valued Neural Networks

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.

Automated summary

This article focuses on the global synchronization and stability of fractional-order quaternion-valued neural networks, proposing multiple and flexible criteria based on the Lyapunov theory and new inequalities. The effectiveness of these criteria is demonstrated through numerical examples.