Finite-Time Synchronization of Chaotic Memristive Multidirectional Associative Memory Neural Networks and Applications in Image Encryption

Traditional biological neural networks lack the capability of reflecting variable synaptic weights when simulating associative memory of human brains. In this paper, we propose a novel memristive multidirectional associative memory neural networks (MAMNNs) model with mixed time-varying delays. More precisely, the proposed model is investigated with time-varying delays and distributed delays. Then, we design two kinds of delay-independent and delay-dependent controllers to analyze the problem of finite-time synchronization. Based on the drive-response concept and Lyapunov function, some sufficient criteria guaranteeing the finite-time synchronization of the drive-response system are derived. With the removal of certain constraints on the weight parameters, the results we obtained for synchronization are less conservative. To illustrate the chaotic characteristics of the memristive MAMNNs, an image encryption scheme is designed. Meanwhile, the effectiveness of the proposed theories is validated with numerical experiments.