Cluster Output Synchronization for Memristive Neural Networks

Herein, cluster output synchronization for memristive neural networks (MNNs) is investigated using two different control schemes. Existing synchronization models for MNNs focus on the behavior of a single neuron node in one-cluster networks. However, actual neural networks (NNs) are clustered organizations consisting of multiple interacting clusters, where the nodes from the same cluster combine and work together. This study proposes a cluster output synchronization model for MNNs, which considers the combination output behavior of the nodes in NNs clusters. Accordingly, two specific control schemes are designed: one based on feedback control involves designing a small number of controllers to reduce control costs, and the other based on adaptive control involves designing multiple adjustable controllers to increase the anti-interference capacity of the control system. Meanwhile, to facilitate synchronization in MNNs, a model relationship between MNNs and traditional NNs is investigated. By utilizing the control schemes, model relationship, and Lyapunov stability theory, sufficient conditions are obtained for validating the cluster output synchronization. Finally, several numerical examples are given to illustrate the accuracy of the theoretical results.