Investigation Of Outer Synchronization Of Complex Networks With Time-Varying Coupling Delay

Within the last decades up to the present time, researchers have eyewitnessed the birth of a new movement in research interest in the study of synchronization of complex networks. The researches based on this subject are pervading almost all disciplines of sci-ences today, including information technology, control science, mathematics, chemistry, physics, medicine, biology, sociology, management, economics, etc. In the dissertation, combining the classical control theory, nonlinear system theory, matrix analysis and al-gebraic graph theory, finite time mixed outer synchronization of complex networks with coupling time-varying delay and outer synchronization of complex networks with multi-coupling time-varying delays are investigated systematically. The main innovative work and key points can be summarized as follows:1. The problems found in finite-time mixed outer synchronization (FMOS) of com-plex networks with coupling time-varying delay have been investigated. FMOS is a re-cently developed generalized synchronization concept, that is, in which different state variables of the corresponding nodes can evolve into finite-time complete synchroniza-tion, finite-time asynchronization, and even amplitude finite-time death simultaneously for an appropriate choice of the controller gain matrix. Some novel stability criteria for the synchronization between drive and response complex networks with coupling time-varying delay are derived by using the Lyapunov stability theory and linear matrix in-equality (LMI). Consequently, a simple linear state feedback synchronization controller is designed. Numerical simulations for two coupled networks of modified Chua’s circuits are then provided to demonstrate the effectiveness and feasibility of the proposed com-plex networks control and synchronization schemes and then compared with the proposed results and previous schemes for accuracy. Simulation results show that the complex net-works with coupling time-varying delay can achieve FMOS.2. The outer synchronization problems encountered in complex networks with mul-tiple coupling time-varying delays have also been investigated. First of all, from some novel synchronization criteria that are obtained by employing the Lyapunov stability the- ory and linear matrix inequality, we design some synchronization controllers to keep the given complex network synchronizing to the object trajectory. Furthermore, an adaptive outer synchronization scheme is derived to achieve a global synchronization, which is simpler than some traditional controllers. Finally, numerical analysis and simulations for the two coupled complex networks which are composed of unified chaotic systems are given to demonstrate the effectiveness and feasibility of the proposed complex network control and synchronization schemes. Simulation results show that the complex networks with multiple time-varying delays can achieve completely an outer synchronization under the influence of an external synchronization controller.Based on this, the results of the dissertation are then summarized and further research topics are recommended.