Predefined-Time Synchronization of Stochastic Memristor-Based Bidirectional Associative Memory Neural Networks With Time-Varying Delays

In this article, we consider the predefined-time synchronization problem of stochastic memristor-based bidirectional associative memory neural networks (MBAMNNs). First, considering the influence of stochastic disturbance, we propose two new predefined-time theorems. Second, combined with the predefined-time theorem proposed in this article, we design a feedback controller to realize the predefined-time synchronization of MBAMNNs. Then, the sufficient conditions for the predefined-time synchronization of MBAMNNs are obtained based on Ito’s formula and Lyapunov theorem. Finally, the effectiveness of the theorems is verified by numerical simulations.

I. Introduction

Nonlinear systems have abundant dynamic behaviors, such as stability, bifurcation, chaos, and so on. The research on its stability and synchronization plays an important role in the fields of secure communication and automatic control [1], [2]. Synchronization of nonlinear systems has always been a hot issue. In 1953, Kanebkov was the first who proposed the concept of the finite-time stability [3], that is, under the action of the controller, the system can reach a stable state in a finite time, but the establishment time of finite-time stability is related to the initial state of the system. In vehicle control, robot tracking control, and other practical applications [4]–[6], accurate initial state is difficult be obtained. In 2012, Polyakov [7] proposed the fixed-time stability to solve this problem. The estimation of the upper bound of the establishment time is independent of the initial state. Therefore, more and more researchers began to invest in the study of fixed-time stability, and tried to find the less conservative upper bound estimate [8]–[11].