Finite‐time synchronization for memristor‐based BAM neural networks with stochastic perturbations and time‐varying delays

Abstract

Summary This paper focuses on the finite‐time synchronization issue of drive‐response memristor‐based bidirectional associative memory neural networks (MBAMNNs) with stochastic perturbations and time‐varying delays. Based on the mathematical model of memristor, definition of finite‐time stability for stochastic differential system and the drive‐response concept, some novel sufficient conditions are given to ensure the finite‐time synchronization of drive‐response MBAMNNs with stochastic perturbations and time‐varying delays. We design novel nonlinear feedback controllers to control the synchronization error to converge zero in a finite time, and the settling time for synchronization can be easily obtained. In addition, as two special cases, the finite‐time synchronization control criteria for bidirectional associative memory neural networks with stochastic perturbations and time‐varying delays and MBAMNNs without stochastic perturbations are also given. Finally, two numerical simulations are showed to demonstrate the correctness of main results.

New results on stability analysis and extended dissipative conditions for uncertain memristive neural networks with two additive time‐varying delay components and reaction‐diffusion terms

“…In recent years, lots of scholars have studied many dynamical behaviors of MNNs. Many kinds of interesting results have been reported in the literature studies, see References 5‐10 and the references therein. In Reference 6, by using the theories of differential inclusions and set‐valued maps, the authors investigated the problem of passivity analysis for uncertain MNNs with time‐varying delays.…”

Finite-Time Synchronization of Multi-Linked Memristor-Based Neural Networks With Mixed Time-Varying Delays

“…Many scholars pay considerable attention to investigating the finte-time synchronization and stabilization of MNNs involving various time delays. And many excellent results have been reported, please see work [47], [49] and the references therein. However, there exist only few related literatures reporting the synchronization and stabilization control of MMNNs, please see [46], [48].…”

“…, m, L h , L g , L f , Ξ h , Ξ g and Ξ f are described in Assumption 1. Then the MMNNs system (2) can be synchronized with (1) under the controller (47) during the settling time t * 3 , given by…”

“…It is of significant importance to study the finite-time synchronization control of MNNs. There have been numerous investigations about finite-time synchronization of MNNs, such as, finite-time synchronization of fractional-order MNNs has been studied in [20], [43], finite-time synchronization of delayed MNNs has been investigated in [44]- [46], finite-time synchronization of bidirectional associative memory MNNs has been studied in [23], [43], [47], etc.…”

“…12 and 6. However, the controller (47) needs more constraints while the controller (63) is much less conservative. In the actual engineering environment, it is very hard to find the appropriate activation functions which satisfy all the constraints, and in the neural networks, it is very hard to mimic the actual activation functions.…”