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Chaotic Secure Communication by Tsinghua University Tsinghua University Press, Kehui Sun

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3Typical Chaotic Systems

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.

3.1Discrete-Time Chaotic Map

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

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