New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality

Abstract

In this paper, a novel kind of neural networks named fractional-order quaternion-valued bidirectional associative memory neural networks (FQVBAMNNs) is formulated. On one hand, applying Hamilton rules in quaternion multiplication which is essentially non-commutative, the system of FQVBAMNNs is separated into eight fractional-order real-valued systems. Meanwhile, the activation functions are considered to be quaternion-valued linear threshold ones which help to reduce the unnecessary computational complexity. On the other hand, based on fractional-order Lyapunov technology, a new fractional-order derivative inequality is established. Mainly by employing the new inequality technique, constructing three novel Lyapunov–Krasovskii functionals (LKFs) and designing simple linear controllers, the global Mittag-Leffler synchronization problems are investigated and the corresponding criteria are acquired for the system of FQVBAMNNs and its special cases such as fractional-order complex-valued BAM neural networks (FCVBAMNNs) and fractional-order real-valued BAM neural networks (FRVBAMNNs), respectively. Finally, two numerical examples are given to show the effectiveness and availability of the proposed results.