Bipartite Synchronization Analysis Of Memristor Neural Network

In this thesis,the bipartite synchronization problems of memristive neural networks are studied,including memristive neural networks with unknown parameters,heterogeneous memristive neural networks and multi-layer memristive neural networks.Combined with pinning control mechanism and adaptive control mechanism,several control strategies are designed.By applying stability theory,theory of linear matrix inequality,and marix theory,several sufficient criteria are obtained to guarantee bipartite synchronization of memristive neural networks.The specific research are listed as follows:(1)By adopting pinning control strategy,the bipartite quasi-synchronization problem of memristive neural networks is studied.Since neural networks are often affected by parameter perturbations,the bipartite quasi-synchronization problems of memristive neural networks with uncertain parameters and heterogeneous memristive neural networks are studied,and the corresponding memristive neural networks are constructed.In order to avoid high cost caused by controlling all nodes,a pinning control strategy is designed to reach bipartite quasi-synchronization by pinning partial nodes of networks.The results show that the bipartite quasi-synchronization can be reached in memristive neural networks by pinning control strategy,and the upper bound of the quasi-synchronization errors are further given.(2)Based on the adoptive strategy,the bipartite synchronization problem of multilayer memristive neural networks under adaptive control is studied.Firstly,a multi-layer network topology with cooperative-competitive relationships is introduced,and the inter-layer and intralayer coupling relationships are also considered.Noting that neural networks are often affected by external disturbances in reality,a multi-layer memristive neural network with unknown parameters and external disturbances is established.Secondly,based on the adaptive control mechanism,Lyapunov function,stability theory,a sufficient criterion for robust bipartite synchronization is obtained.(3)Furthermore,combining pinning control and adaptive control strategies,the bipartite quasi-synchronization problem of memristive neural networks are studied.For a memristive neural network with unknown parameters and external disturbances is established over the multi-layer signed network topology,a pinning adaptive control strategy is designed based on the pinning control and adaptive control mechanism.By utilizing the Lyapunov function and stability theory,a sufficient criterion for robust bipartite quasi-synchronization is obtained,and an upper bound of the synchronization errors is given.