New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality. (February 2020)

• Record Type: Journal Article
• Authors: Xiao, Jianying; Wen, Shiping; Yang, Xujun; Zhong, Shouming
• Is Part Of: Neural networks. Volume 122(2020)
• Page Start: 320
• Page End: 337
• Publication Date: 2020-02
• Subjects: Fractional-order system -- Quaternion-valued neural networks -- Bidirectional associative memory -- Mittag-Leffler synchronization; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2019.10.017
• Languages: English
• ISSNs: 0893-6080

Abstract

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.