Synchronization Analysis Of Discrete-time And Uncertain Dynamical Networks

When the small-world and scale-free networks were born, complex networks haveattracted more and more attention. Presently the main issues of complex networks havebeen their topological structures, dynamics and applications. It has been proven as apowerful tool to describe complex systems, where the complexity is reflected in nodes,connections and as a whole. Synchronization of complex networks is a hot topic, focus-ing on the efect of the topologies and node dynamics on the synchronization. When thesynchronization is not achieved under appropriate topologies and node dynamics, somecontrollers are designed to realize the synchronization. In this dissertation, the main workis to study the synchronization of complex networks, including discrete-time and uncer-tain networks. Finally, we obtain the criteria of synchronization. In details, the maincontents are as follows:Based on Lyapunov stability theory, Chapter II studies the synchronization betweentwo discrete-time networks with mutual coupling and obtains a sufcient condition toachieve network synchronization. We use some numerical examples to verify the correct-ness and validity of the theoretical analysis, which indicates that the inner synchronizationis easier to be achieved than outer synchronization. In addition, given the mutual couplingmatrix and the corresponding node dynamics, the inner and outer synchronization can besimultaneously achieved by adjusting the coupling strength.In Chapter III, we study the synchronization of Driver-Response networks in discrete-time chaotic systems. The outer synchronization between two networks via contractiontheory is achieved. The numerical simulations are given to illustrate the theoretical efec-tiveness.Chapter IV investigates generalized outer synchronization between two uncertaindynamical networks, where the coupling of each network is described by a nonlinearfunction. We design appropriate controllers to realize generalized outer synchroniza-tion. Finally, numerical simulations are given to verify the efectiveness of the controllers.Chapter V makes a brief summary and presents some problems for further studies.