Mittag-Leffler synchronization and stability analysis for neural networks in the fractional-order multi-dimension field

This paper proposes the relaxed criteria about the problem of synchronization and stability for the same category fractional-order system of multidimension-valued neural networks (FOSMVNNs). First, we uniformly formulate a new class of FOSMVNNs. Based on Hamilton rules, the researched FOSMVNNs are effectively separated into the four or two fractional-order systems of real-valued neural networks (FOSRVNNs). Moreover, we infer a novel inequality with the quadratic term which distinguishes the new inequality from the existing ones and apply it in the new analysis on the synchronization and stability problem for FOMVNNs. On the basis of the new inequality, some new Lyapunov-Krasovskii functionals (LKFs) and the relaxed criteria can be successfully constructed with quadratic coefficients which can be effectively used for the studied systems mainly via fractional-order Lyapunov method. Finally, we present two numerical simulations to show the possibility and improvement of the obtained relaxed criteria