Novel methods to finite-time Mittag-Leffler synchronization problem of fractional-order quaternion-valued neural networks

Abstract This paper proposes two methods to investigate the problem of finite-time Mittag-Leffler synchronization for the systems of fractional-order quaternion-valued neural networks (FQVNNs) with two kinds of activation functions, respectively. Generally, the first method mainly reflects in the new establishment of Lyapunov-Krasovskii functionals (LKFs) and the novel application of a new fractional-order derivative inequality which contains and exploits the wider coefficients with more values. Meanwhile, the second one is embodied in the comprehensive development of both the norm comparison rules and the generalized Gronwall-Bellman inequality with the help of Laplace transform of Mittag-Leffler function. Thanks to the above two methods, the flexible synchronization criteria are easily and separately obtained for the studied four systems of FQVNNs with general activation functions and linear threshold ones. Finally, two numerical simulations are given to demonstrate the feasibility and effectiveness of the newly proposed approaches.

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