Projective Synchronization of Nonidentical Fractional-Order Memristive Neural Networks

Abstract

This paper investigates projective synchronization of nonidentical fractional-order memristive neural networks (NFMNN) via sliding mode controller. Firstly, based on the sliding mode control theory, a new fractional-order integral sliding mode controller is designed to ensure the occurrence of sliding motion. Furthermore, according to fractional-order differential inequalities and fractional-order Lyapunov direct method, the trajectories of the system converge to the sliding mode surface to carry out sliding mode motion, and some sufficient criteria are obtained to achieve global projective synchronization of NFMNN. In addition, the conclusions extend and improve some previous works on the synchronization of fractional-order memristive neural networks (FMNN). Finally, a simulation example is given to verify the effectiveness and correctness of the obtained results.

Finite-time Mittag–Leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions*

“…Remark 1 The relevant dynamic behaviors of fractionalorder memristive neural networks have been investigated in Refs. [22][23][24]. However, the activation functions are Lipschitz-continuous and satisfy f j (±T j ) = g j (±T j ) = 0.…”

“…In addition, to the best of our knowledge, the activation functions of many literature [17,[22][23][24] were assumed to be Lipschitz, continuous or continuously differentiable. However, the activation functions of FMNN are usually discontinuous.…”

“…[29][30][31] However, asymptotic synchronization denotes that it takes infinite time from the trajectories of the response to the trajectory of the drive system. [22,23,32,33] In fact, it is more desirable for networks to reach synchronization in a finite-time and achieve optimization in convergence time in physical and engineering. [34][35][36] Hence, it is necessary to investigate the finite-time synchronization of FMNN.…”

Quasi-Synchronization of Nonidentical Fractional-Order Memristive Neural Networks via Impulsive Control

“…Scholars introduce fractional calculus into the study of MNNs and formed fractional-order memristive neural networks (FMNNs) model [14][15][16]. FMNNs can describe the memory properties of neurons more accurately and achieve many results in synchronization and stability [17][18][19][20]. e global Mittag-Leffler stabilization of a class of FMNNs with time delays was discussed under a state feedback control in [17].…”

“…e global Mittag-Leffler stabilization of a class of FMNNs with time delays was discussed under a state feedback control in [17]. Chen and Ding [20] via a sliding mode controller and fractional-order Lyapunov direct method studied projective synchronization of nonidentical FMNNs.…”