Outer Synchronization Between Uncertain Time-varying Delayed Networks With Diverse Structures

In the fields of information communication and engineering technology,synchronization phenomena of complex dynamic networks are very common.The related researches on synchronization of complex networks focus mainly on those networks with the relatively simple and regular topologies.With the in-depth understanding of the actual network structures,the investigated networks for synchronization are getting closer and closer to practice ones because there exist many new characteristics,such as the large number of nodes,the complex connection,the uncertain topological structure,and so on.In this thesis,the synchronization behaviors of time-varying dynamic networks with unknown parameters are mainly researched.Firstly,the coupling outer synchronization of time-varying complex networks with diverse structures and delay times is investigated;and then the network model discussed in the time domain is extended to the spatiotemporal network,and the synchronization problem of the spatiotemporal dynamic network with diverse structure nodes tracking the target system is further studied.The main research works of this thesis are as follows:In the first chapter,the related concepts,research background,investigation significance and the typical models of dynamic complex networks are introduced briefly.Finally,the development of the research works in the field of complex networks at the home and abroad is analyzed.In the second chapter,the types of network synchronization and the related criterions of synchronization are summarized and then,the actual application of complex network synchronization is illustrated.In addition,the existing related works of network synchronization are also introduced in the last part of this chapter because the problem of network synchronization is our main work in this thesis.In the third chapter,outer synchronization behavior between two uncertain time-varying delayed networks with diverse structures is discussed and investigated.Based on Lyapunov stability theory,the outer synchronization between two uncertain dynamic networks with diverse structures is achieved by adopting the bidirectional coupling adaptive method.And the network topology and coupling strength can be identified simultaneously in the synchronization process.In the numerical simulation,Van der Pol systems and Duffing systems are taken as nodes to construct the networks and the simulation results show that the method proposed in this work is effective and reliable.In the fourth chapter,the tracking synchronization of spatiotemporal dynamic complex networks with different structures is investigated.The chaos dynamic equation of node isfirstly extended from the time domain to spatiotemporal domain.Then based on Lyapunov stability theory,the controller structures are gained and the mechanism of tracking synchronization and the updating rules of unknown parameters within the response network are determined through designing an appropriate Lyapunov function.Finally,Fisher-Kolmogorov systems with spatiotemporal behaviors are taken as nodes to construct the spatiotemporal dynamic complex networks with uncertain parameters and the NS-Burgers spatiotemporal chaotic system is taken as target system.The numerical simulation is performed and the feasibility of tracking control theory is verified.In the last chapter,the research works in this thesis are summarized,and the prospects on the further research about the outer synchronization problem of complex dynamic networks and on the application potential are proposed.