Abstract

This paper investigates the existence and structure of one-dimensional discrete chaotic systems. It is expected to change the research perspective of discrete chaotic system, from being passively discovered to actively constructing. Firstly, some sufficient conditions guaranteeing a one-dimensional discrete system being chaotic are proposed and rigorously proved. Secondly, it presents a simple method for constructing the one-dimensional discrete chaotic system which can provide more models and inspecting tools for the study of the latter. Finally, by applying the method, some new discrete chaotic systems are constructed, and the numerical results with the bifurcation diagram and the Lyapunov exponent illustrate the chaos, which thus verifies the feasibility and effectiveness of the proposed method.

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