Finite-time and fixed-time self-triggered synchronization of stochastic memristive neural networks and applications in secure communication.

Abstract

The dynamic characteristics of memristive neural networks (MNNs) can be affected by multiple environmental factors. With that in mind, this paper simultaneously considers the comprehensive effects of stochastic disturbance, external input and actuator hysteresis on the MNNs. Firstly, the driving-response stochastic MNNs (SMNNs) subjected to external inputs and hysteresis are introduced, along with a class of secure communication schemes constructed based on this system. Next, definitions of asymptotically, finite-time, and fixed-time synchronization in probability for the considered system are proposed. Following, some synchronization strategies are given by using the self-triggered control method and Lyapunov stability theories. The designed controllers can ensure the finite-/fixed-time synchronization in probability of the SMNNs, as well as the asymptotically synchronization of the secure communication system. Finally, three simulations and comparative experiments demonstrate the proposed strategies' effectiveness.