Abstract
The chaotic system is widely used in chaotic cryptosystem and chaotic secure communication. In this paper, a universal method for designing the discrete chaotic system with any desired number of positive Lyapunov exponents is proposed to meet the needs of hyperchaotic systems in chaotic cryptosystem and chaotic secure communication, and three examples of eight-dimensional discrete system with chaotic attractors, eight-dimensional discrete system with fixed point attractors and eight-dimensional discrete system with periodic attractors are given to illustrate how the proposed methods control the Lyapunov exponents. Compared to the previous methods, the positive Lyapunov exponents are used to reconstruct a hyperchaotic system.
Highlights
The Lyapunov exponent is a numerical characteristic that represents the average exponential divergence rate of adjacent trajectories in phase space, and it is one of the numerical characteristics used to determine chaotic behavior
The chaotic behavior of the chaotic system is of vital importance to determine the security of chaotic cryptosystem and chaotic secure communication
If low-dimensional chaotic systems and high-dimensional chaotic systems have the same number of positive Lyapunov exponents, the complexity of their chaotic behavior will be quite similar
Summary
The Lyapunov exponent is a numerical characteristic that represents the average exponential divergence rate of adjacent trajectories in phase space, and it is one of the numerical characteristics used to determine chaotic behavior. In 1996, Chen proposed the chaos feedback control method to control the number of positive Lyapunov exponents in the discrete chaotic system [Chen & Lai, 1996]. On this basis, Yu proposed a universal design of a discrete chaotic system with the most positive Lyapunov exponents [Lin et al, 2015], and the design result of the eight-dimensional discrete chaotic system is given. A design method of discrete chaotic systems with any desired number of positive Lyapunov exponents is proposed. A Discrete Chaotic Design Method for any Desired Number of Positive Lyapunov Exponents
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