In this paper, we consider the predefined-time synchronization problem of stochastic memristor-based bidirectional associative memory neural networks (MBAMNNs). Firstly, considering the influence of stochastic disturbance, we propose two new predefined-time theorems. Secondly, combined with the predefined-time theorem proposed in this paper, 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 are verified by numerical simulations.

This paper explores the realization of a predefined-time synchronization problem for coupled memristive neural networks with multi-links (MCMNN) via nonlinear control. Several effective conditions are obtained to achieve the predefined-time synchronization of MCMNN based on the controller and Lyapunov function. Moreover, the settling time can be tunable based on a parameter designed by the controller, which is more flexible than fixed-time synchronization. Then based on the predefined-time stability criterion and the tunable settling time, we propose a secure communication scheme. This scheme can determine security of communication in the aspect of encrypting the plaintext signal with the participation of multi-links topology and coupled form. Meanwhile, the plaintext signals can be recovered well according to the given new predefined-time stability theorem. Finally, numerical simulations are given to verify the effectiveness of the obtained theoretical results and the feasibility of the secure communication scheme.