Synchronization Analysis For Complex Networks With Double Time-varying Delays

Synchronization of complex networks, which forms some kind of overall coherencebetween the dynamical systems through the interactions, is one of the most common dynamicalbehaviors. Currently, synchronization of the complex networks has got attention of scholars fromdifferent fields. This paper mainly uses the Lyapunov functional method and linear matrixinequality to study synchronization problem of complex networks，where the out-couplingmatrix of complex network with double constant time delays is assumed to be symmetric andirreducible, or the out-coupling matrix of complex networks with double time-varying delays isassumed to be non-symmetric and reducible.The first chapter introduces an overview of the complex network applications, researchstatus and development trends in China and abroad, as well as the overall structure and some ofinnovations. The second chapter gives the relevant preliminary knowledge, including therelevant definitions and the lemmas to be used. In the third chapter, synchronization problem forcomplex networks with double constant time delay is studied, in which the restriction on theout-coupling matrix of complex networks is symmetric and irreducible. Based on Lyapunovstability theory and linear matrix inequalities, the sufficient condition of synchronization stabilityis developed by constructing appropriate Lyapunov functionals. In the fourth chapter,synchronization problem for general complex networks with double time-varying delays isstudied, in which the restriction on the out-coupling matrix of complex networks is symmetricand irreducible. Based on Lyapunov stability theory and linear matrix inequalities, the sufficientcondition of synchronization stability is developed by constructing appropriate Lyapunovfunctionals. In the fifth chapter, synchronization problem for general complex networks withdouble time-varying delays is studied, in which the restriction on the out-coupling matrix ofcomplex networks is non-symmetric and reducible. Complex eigen-values and complex vectorsare dealt with. Based on Lyapunov stability theory and linear matrix inequalities, the sufficientcondition of synchronization stability is developed by constructing appropriate Lyapunovfunctionals. Through chapter three to five, numerical examples are employed to verify theeffectiveness and feasibility of the results.