| Chaos synchronization plays a pivotal role in chaos studies. In resent decades, chaos synchronization has been extensively and intensively studied due to its potential applications in secure communication, information science and so on, moreover, it has become a focal issue in modern nonlinear scientific research. Based on Lyapunov method, the stability theory for impulsive functional differential equations, inequality technique, the thesis addresses control and application of chaos synchronization for several classes of chaos systems which include drive-response dynamical networks, drive-response dynamical networks with coupling delays, drive-response time-delaying dynamical networks. This thesis comprises five chapters and the main results are as follows.In the first chapter of this thesis, the general background of chaos theory is given, and the significance of studies on chaos theory is introduced. Also the main contents and significance of this dissertation are generalized.In the second chapter, the projective synchronization of drive-response complex dynamical networks is investigated. To control projective synchronization of chaotic systems in a preferred way, an impulsive control scheme is adapted to direct the scaling factor onto a desired value. By using the stability theory of the impulsive differential equation, the criteria for the projective synchronization are derived. The feasibility of the impulsive control of the projective synchronization is demonstrated in simulation examples.In the third chapter, the projective synchronization in the drive-response dynamical networks with coupling delays is discussed. First, the drive-response dynamical networks where the response system consist of delay coupled chaos systems is introduced. The suitable impulsive controller allow the system synchronize the drive-response dynamical networks to a desired scalar factor. Some criteria are derived by employing suitable Lyapunov method. The control method generalizes the result in the proffer literature.In the forth chapter, the projective cluster synchronization problem of complex networks is studied. The effects of coupling scheme satisfying some conditions are considered in realizing cluster synchronization. The cluster synchronization with desired scaling factors can be exponentially achieved in the drive-response system consisting N + 1 nodes via impulsive control method. Server sufficient conditions are derived. Numerical simulations are provided to demonstrate the effectiveness of the proposed control method.In the fifth chapter, the projective synchronization of time-varying complex networks is investigated, we consider synchronization in time-varying coupling networks, in which the weights of links are time varying. Based on a useful approach–the matrix measure, some simple but generic criteria for exponential synchronization of time-varying complex networks are obtained. It is showed that the obtained results are easy to verify and simple to implement in practice. Theoretical analysis and numerical simulations of complex networks based on Lüsystem verify our main results.
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