| Inner synchronization and outer synchronization control of complex dynamical networks are investigated in this paper. Some network models are mainly studied, such as the complex networks with time-varying topological structures and multiple coupling delays, nonlinearly time-varying delays coupled complex networks, nonlinearly time-varying delays coupled complex networks with time-varying delays in dynamical nodes and time-varying coupling strengths, cluster synchronization in nonlinearly and linearly time-varying delays coupling complex dynamic networks with nonidentical time-varying delay dynamical nodes, complex dynamical networks with uncertain parameters and disturbance, et al. We use variable feedback control, adaptive control, pinning control and impulsive control methods to study the synchronization control problem of these complex dynamical networks, and obtain some criteria to realize complete synchronization, cluster synchronization, cluster projection synchronization, cluster anti-synchronization and lag synchronization, et al. Numerical simulations are given to illustrate the effectiveness of the results.This paper is composed of eight chapters. In chapter1, we introduced the background briefly and study progress of complex networks and synchronization control. Main results and ideas were given from Chapter2to Chapter7. Some existing problems as well as the future research were pointed out in Chapter8. The main research work of this thesis has several parts as follows:1. Synchronization of time-varying complex dynamical network is investigated,we consider synchronization in time-varying coupling networks with time-varying topological structures and multiple coupling delays,nonlinearly time-varying delays coupled complex networks by pinning control. We investigate pinning synchronization of nonlinearly coupled complex networks with time-varying coupling delay and time-varying delay in dynamical nodes by adaptive feedback controllers and adjusting time-varying coupling strengths, to ensure the nodes in the networks synchronization, also.2. Impulsive synchronization between two coupled complex delayed networks with time-delayed dynamical nodes is investigated, based on the Lyapunov stability theory and the generalized Barbalat’s lemma, linear feedback control theory and impulsive control theory. The linear feedback controller and impulsive controller are designed respectively, global asymptotic impulsive synchronization of the drive-response complex networks are derived. Particularly, the weight configuration matrix is not assumed to be symmetric, irreducible or dissipative, and the inner coupling matrix need not be symmetric. Numerical examples are presented to verify the effectiveness and correctness of the synchronization criteria.3. Cluster synchronization in the time-varying delays coupling complex dynamical networks with nonidentical nodes and time-varying coupling strengths is investigated. By controlling the nodes in one community which have direct connections to the nodes in other communities strategy and adjusting time-varying coupling strengths, some sufficient criteria are derived to ensure cluster synchronization. A new cluster synchronization scheme in the nonlinear coupled complex dynamical networks with nonidentical nodes is investigated also. Basing on the community structure of the networks, the controllers are designed differently between the nodes in one community which have direct connections to the nodes in other communities and the nodes without direct connections with the nodes in other communities strategy, some sufficient criteria are derived 4. Lag synchronization of nonlinear coupled complex networks is investigated via pinning control, where the coupling strength is an invariable constant. By adjusting pinning control strength, some sufficient conditions of lag synchronization are obtained by using the Lyapunov direct method. The controllers to ensure that the special networks could get lag synchronization. The pinning nodes can be randomly selected. It indeed provides some new insights for the future practical engineering design.5. A general function projective synchronization scheme is proposed for complex dynamical networks with uncertain parameters and disturbance. Not only unknown parameter of the networks is estimated by adaptive laws obtained from Lyapunov stability theory and Taylor expansions, but also unknown bounded disturbances can be simultaneously conquered by use of the updating laws. In addition numerical simulations were performed to verify the effectiveness of the theoretical results.6. Cluster projective synchronization and cluster anti-synchronization scheme in the time-varying delays coupled complex dynamical networks with nonidentical nodes are investigated. Basing on the community structure of the networks, the controllers are designed differently between the nodes in one community which have direct connections to the nodes in other communities and the nodes without direct connections with the nodes in other communities strategy. According to Lyapunov stability theory and LaSalle invariance principle, some sufficient criteria are derived to ensure the nodes in the same group projective synchronize with each other and there is also projective synchronization between nodes in different groups and some sufficient criteria are derived to ensure the nodes in the same group anti-synchronization, also.7. At last, some meaningful results are summarized in the end of this paper. Furthermore, some existing problems as well as the future work are pointed out. |
PDF Full Text Request