Synchronization Of Uncertain Multi-link Networks And Cluster Networks

So far,the research about the related issues of complex network has aroused wide attention from scholars both at home and abroad.At the same time,as one of the hot topics in the research field,the synchronization problem of complex networks has attracted great interest.The main reason is that synchronization phenomena exist in various fields of nature and are of comprehensive application values.In this thesis,the coupled chaotic synchronization of multi-link networks and the synchronization of uncertain cluster networks have been mainly investigated.In the first chapter,the generation,basic types and research status of complex networks are introduced briefly.In the second chapter,the synchronization types of complex networks are illustrated.Furthermore,two basic methods(i.e.,Lyapunov exponent method and Lyapunov function method)for determining network synchronization are also discussed.Finally,some applications of network synchronization in actual production are introduced briefly.In the third chapter,the coupling synchronization of uncertain multi-link networks with arbitrary structures is investigated.The synchronization between the network and the target system is achieved by the way of unidirectional coupling,and the identification rules of the coupling coefficients belonging to node state equations and the uncertain parameters are also obtained.Subsequently,the Jaynes-Cumming models in quantum optics are chosen as the state equations of the network nodes to construct the complex network with arbitrary topology.And the correctness and effectiveness of the designed synchronization principle are verified by numerical simulations.In the forth chapter,the cluster synchronization of complex networks in which every nodes are of different dynamical behaviors is studied based on the splitting idea gained in the above chapter.An exponent term is added into the Lyapunov function in order to realize the cluster synchronization between complex networks and in the meanwhile,the uncertain parameters can also be identified effectively.Finally,the forced Busselator model,Van der Pol system and Duffing system are selected as the state equations of each cluster network node to test the synchronization principle through simulation.In the last chapter,the summary of the research contents of this thesis is given,and at the same time some prospect and consideration in the future are put forward.