| Synchronization, as a natural phenomenon, means that two or more systems,which are either periodic or chaotic, adjust to each other and eventually reach com-mon dynamical behavior. Research on chaos synchronization is not only of greattheoretical values but of many practical applications. In recent decades, chaossynchronization has been extensively and intensively studied due to it's potentialapplications in secure communication. This paper mainly address the problemof complete synchronization with impulsive control, and modified projective syn-chronization (MPS) with uncertain parameter for chaotic R(o|¨)ssler system. Basedon the MPS ,a new control method is proposed to stabilize the chaotic R(o|¨)sslersystem. This paper is organized as follows:Chapter 1 is devoted to the history, two definitions, characteristics of chaos,and three routes leading to chaos as well.Next, in Chapter 2, we introduced several kinds of chaos synchronization andsome classical methods of synchronization control. The application of synchro-nization are also presented before introducing the dynamical behavior of R(o|¨)sslersystem.In Chapter 3, impulsive synchronization for R(o|¨)ssler system is studied basedon the theory of impulsive di?erential equation. Moreover, we investigate theconfidential method based on chaotic synchronization with impulsive control.In the fourth chapter, we propose a control method for the MPS with param-eters unknown and also illustrate its e?ectiveness by numerical simulation.Finally, in Chapter 5, based on the MPS, an e?cient control method is pro-posed to achieve chaos control.
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