Fixed-time synchronization control of memristive MAM neural networks with mixed delays and application in chaotic secure communication

In this paper, the fixed-time synchronization control problem of memristive multidirectional associative memory neural networks (MMAMNNs) is considered. Based on the nonlinear and chaos characteristics of memristor, a chaotic model is constructed. And then, utilizing the Lyapunov stability theory, two appropriate controllers are constructed and different activation functions are used. This control method ensures that drive system and response system can achieve synchronization within a fixed time. So, compared with previous studies, it has more practical value. In addition, we present a fixed-time synchronization chaotic encryption method, the chaos characteristic of the model is used to encrypt plaintext, and the decryption of ciphertext is realized based on the synchronization control theories. Finally, several numerical simulations are given to demonstrate the validity of the theories and the chaotic secure communication scheme.