Spatiotemporal Synchronization Of Time-delay Networks With Uncertain Topological Structure And Different Nodes

Network synchronization is one of the main contents of network dynamics research,and its synchronous mode can be divided into inter synchronization and outer synchronization.Among them,the outer synchronization of the network has attracted the attention of international and domestic scholars because of its unique application potential in many fields.At the same time,there are many uncertainties in the network topology,node dynamics and network parameters in the outer synchronization process,which will affect the synchronization performance of the network.Therefore,this thesis studies the uncertain topology and the outer synchronization of time-delay networks with different nodes,the main tasks are as follows:The outer synchronization of discrete time-delay spatiotemporal networks with unknown topology is studied.Applying the linear matrix inequality principle and the Lyapunov theorem,by constructing a suitable Lyapunov function,the structure of the network controller and the adaptive law of the coupled matrix elements are determined,and the conditions for realizing the outer synchronization between time-delay networks with unknown topology are obtained.Finally,the one-dimensional Logistic spatiotemporal model is used as the network node for numerical simulation to verify the rationality of the designed outer synchronization scheme.Furthermore,the outer synchronization of uncertain continuous time-delay spatiotemporal networks with different nodes is studied.By constructing a suitable Lyapunov function,the structure of the network controller is determined,and the conditions for realizing the synchronization of two uncertain time-delay spatiotemporal networks with the same topology are obtained.At the same time,the adaptive law of uncertain parameters and configuration function is designed.Finally,two different neuron models are used as nodes to construct spatiotemporal networks with random connections.Numerical simulations verify the effectiveness of the designed outer synchronization scheme.The synchronization scheme designed in this thesis is suitable for network with arbitrary topology,and considers the uncertainty of network parameters and the time-delay effect of coupling between network nodes,so it has certain practicability.