Introduction and Preliminary Knowledge

As a branch of dynamic system, the chaotic system is closely connected with nature and people’s life [1–4]. At present, the chaotic system has been widely used in biology, finance and engineering and other disciplines [5–7]. It is closely related to fractal geometry, mixed and pure theory, bifurcation theory and other fields, and is the focus of current research [8, 9]. Synchronization of the chaotic system and its application to secure communication is an interesting research area [10–12], and it has attracted broad attention [13]. Some preliminary knowledge such as chaos definition and characters, chaos synchronization, chaos control and some important theorems are introduced in this chapter.