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<p>In this paper, a class of one-dimensional discrete chaotic map criterion theorem and five corollaries are proposed by using the Li-Yorke theorem, which gives the chaotic system and its chaotic intervals, multiple chaotic systems are constructed by using the Marotto’s theorem, and the correctness of the theorem is verified by analysing the bifurcation and Lyapunov exponent of the system. When chaotic systems are implemented in finite domains, degradation of the chaotic behaviour is inevitable. Comparing state-mapping networks (SMNs) proposed in this paper with the logistic map, it is found that the maximum period generated by this system under different accuracies is higher than that of the classical logistic chaotic system, which can be analysed from the state network transfer system and the upper limit system of node difference under different accuracies, which has a scale-free nature; and its characteristics can be kept unchanged under different accuracies. Based on the above chaotic system, a pseudo-random number generator is designed, and the generated sequence has good randomness; it has passed the tests of NIST SP800 and TestU01, which complies with cryptography usage criteria.</p>

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Design of dynamics analysis of some one-dimensional discrete chaotic systems

  • 期刊论文

  • 发表日期：

    2025年6月5日

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  • Xu Jia,
  • Hongyan Zang,
  • Xinyuan Wei

摘要

In this paper, a class of one-dimensional discrete chaotic map criterion theorem and five corollaries are proposed by using the Li-Yorke theorem, which gives the chaotic system and its chaotic intervals, multiple chaotic systems are constructed by using the Marotto’s theorem, and the correctness of the theorem is verified by analysing the bifurcation and Lyapunov exponent of the system. When chaotic systems are implemented in finite domains, degradation of the chaotic behaviour is inevitable. Comparing state-mapping networks (SMNs) proposed in this paper with the logistic map, it is found that the maximum period generated by this system under different accuracies is higher than that of the classical logistic chaotic system, which can be analysed from the state network transfer system and the upper limit system of node difference under different accuracies, which has a scale-free nature; and its characteristics can be kept unchanged under different accuracies. Based on the above chaotic system, a pseudo-random number generator is designed, and the generated sequence has good randomness; it has passed the tests of NIST SP800 and TestU01, which complies with cryptography usage criteria.