Chaos exists widely in nature. During the research and development of chaos theory, researchers found a lot of chaotic dynamics models, and some of them are typical for the chaos theory and application research, including discrete-time chaotic maps, continuous-time chaotic systems, and hyperchaotic systems. In this chapter, we will discuss the mathematical model and its main characteristics of some typical chaotic systems.
First, the definition of discrete-time chaotic map is presented. Consider a nonlinear system
where “○” represents a compound operation between two functions. x(k) ∈M⊂