Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with time delays.

Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with time delays

Finite-time synchronization of quaternion-valued neural networks with delays: A switching control method without decomposition

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.

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

This paper is devoted to discussing the globally projective synchronization of Caputo fractional-order quaternion-valued neural networks (FOQVNNs) with discrete and distributed delays. Without decomposing the FOQVNNs into several subsystems, by employing the Lyapunov direct method and inequality techniques, the algebraic criterion for the globally projective synchronization is derived. The effectiveness of the proposed result is illustrated by the MATLAB toolboxes and numerical simulation.

Globally projective synchronization for Caputo fractional quaternion-valued neural networks with discrete and distributed delays

In this article, the finite time (FT) synchronization problem of fractional order quaternion valued neural networks with time delay is investigated. Without separating the quaternion valued system into two complex valued or four real valued systems, the FT synchronization conditions are derived through using Lyapunov direct method. Furthermore, the setting time is estimated, which is influenced by the order of fractional derivative and control parameters. Finally, numerical simulations are shown to verify the effectiveness of the proposed methods.

Weiwei Zhang

Papers

Finite Time Synchronization of Delayed Quaternion Valued Neural Networks with Fractional Order

Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field