Synchronization of memristive neural networks with two types of delays and application to secure communication

This paper investigates the synchronization and control of memristive neural networks (MNNs) with time-varying and distributed delays. First, the existence of a unique equilibrium point for MNNs is proven using the homeomorphism theory. By employing inequality technique, a new lemma is proposed which is used to prove MNNs are exponentially stable. Then, the error of the drive–response system is studied through Lyapunov method. By utilizing feedback controllers and adaptive controllers, we have derived the conditions necessary for achieving synchronization in the drive–response system of MNNs. These conditions are presented in the form of Linear Matrix Inequalities (LMIs). Additionally, through comparative experiments, the feedback controller designed in this paper enables faster convergence of MNNs, and the adaptive controller designed is applicable to a larger range of delays. Finally, three numerical examples are provided to demonstrate the effectiveness of the theoretical results and their applicability to secure communication.