Master–slave synchronization of fractional-order memristive MAM neural networks with parameter disturbances and mixed delays

Abstract

In order to describe the system as realistically as possible, the fractional-order memristive multidirectional associative memory neural networks (FOMMAMNNs) with parameter disturbances, time-varying and distributed delays are established. Further, the master–slave synchronization is explored. Firstly, in the Filippov’s sense, some conditions are derived via the contraction mapping principle to guarantee the uniqueness of equilibrium point of the system. Secondly, from the perspective of reducing control costs, pinning controller and adaptive pinning controller are designed for the first time to induce synchronization of FOMMAMNNs. Moreover, some synchronization criteria are obtained by using the properties of fractional calculus, the appropriate Lyapunov candidate functions and fractional Barbalat’s lemma. Thirdly, a communication scheme based on chaotic synchronization is proposed to achieve the safe transmission of important information. Finally, two numerical simulations are given to illustrate the feasibility of the theoretical results and the security of the designed communication scheme.