Abstract
This dissertation is constituted of two parts. The first part mainly treats of the synchronization in the nearest neighbor linear coupling chaotic dynamical systems and its associated phenomena. The majority of the second part concerns with the application of the generalized synchronization concept in dealing with chaotic control problems arising in chaotic systems.There are two types of dynamical systems to be considered in the first part. One is of discrete type and the other is of continuous type. For discrete dynamical systems, we use the Logistic equation as the major topic to be discussed. Then we have the following results：if the nearest neighbor linear coupling method is adopted, the synchronization phenomenon would gradually become disappeared when the number pf coupled nodes increases. As to the continuous dynamical systems, we pay our attention major in the study of the synchronization phenomena in three-dimension chaotic dynamical systems. We do deeper study on the famous the Lorenz chaotic system and obtain that it suffices to couple some particular one-dimensional state to obtain the synchronization phenomenon.In the second part, we use the generalized synchronization concept to treat chaotic control problems. As an exampled, we consider the problem of controlling the Lorenz chaotic attractor into non-chaotic state. Beside, we extend this idea to construct the Lorenz unstable periodic solutions by utilizing computers.