Study On Adaptive Synchronization Of Complex Dynamical Networks

Complex networks describe a wide range of systems in nature and society area,such as a cell,a mobile communication networks,a computer network,or the World Wide Web. Since the world we lived is filled of different kinds of complex networks,the research works of complex network have been paid more and more attentions.Especially,the research of the synchronization of complex network is a hot topic.The complex network synchronization problems have been studied from many different perspectives.The study on synchronization of complex network with unknown function or unknown coupling function is one important theme.Since any real system has different degree of uncertainty and the mathematical model describes the object or the description of its environment is not established sufficiently.There have been some research results about synchronization problem achieved in and abroad,however,the time-delay factor widely exists in the real world system has been considered in most existed papers which are locally coupled.In the thesis,the synchronization problem of uncertain dynamical network system has been researched based on Lyapunov stability theorem and adaptive theory.The synchronization controller of complex networks and the adaptive controller of synchronization of complex networks are designed respectively under the circumstances of known parameters and unknown parameters,the sufficient condition of network synchronization is given to guarantee that dynamical network asymptotically synchronize as well as.In addition,the method is used in the research of the synchronization problem about uncertain dynamical network model with time-delay nodes;the sufficient condition of network synchronization is also given to guarantee the time-delay dynamical network can asymptotically synchronize.Numerical simulation results indicate that the proposed theorem and conclusions are correct and effective.