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一类2次多项式混沌系统的均匀化方法研究

臧鸿雁 黄慧芳 柴宏玉

臧鸿雁, 黄慧芳, 柴宏玉. 一类2次多项式混沌系统的均匀化方法研究[J]. 电子与信息学报, 2019, 41(7): 1618-1624. doi: 10.11999/JEIT180735
引用本文: 臧鸿雁, 黄慧芳, 柴宏玉. 一类2次多项式混沌系统的均匀化方法研究[J]. 电子与信息学报, 2019, 41(7): 1618-1624. doi: 10.11999/JEIT180735
Hongyan ZANG, Huifang HUANG, Hongyu CHAI. Homogenization Method for the Quadratic Polynomial Chaotic System[J]. Journal of Electronics & Information Technology, 2019, 41(7): 1618-1624. doi: 10.11999/JEIT180735
Citation: Hongyan ZANG, Huifang HUANG, Hongyu CHAI. Homogenization Method for the Quadratic Polynomial Chaotic System[J]. Journal of Electronics & Information Technology, 2019, 41(7): 1618-1624. doi: 10.11999/JEIT180735

一类2次多项式混沌系统的均匀化方法研究

doi: 10.11999/JEIT180735
基金项目: 中央高校基本科研业务费专项基金(06108236)
详细信息
    作者简介:

    臧鸿雁:女,1973年生,副教授,研究方向为非线性系统统同步理论与混沌密码学

    黄慧芳:女,1991年生,讲师,研究方向为混沌密码学

    柴宏玉:女,1990年生,硕士生,研究方向为非线性系统统同步理论与混沌密码学

    通讯作者:

    黄慧芳 13661363592@163.com

  • 中图分类号: TN918.1

Homogenization Method for the Quadratic Polynomial Chaotic System

Funds: The Fundamental Research Funds for the Central Universities of China (06108236)
  • 摘要: 该文给出了一般的2次多项式混沌系统与Tent映射拓扑共轭的充分条件,并依据该条件,给出了一类2次多项式混沌系统及其概率密度函数;进一步得到了能够将这类系统均匀化的变换函数;给出了一个新的2次多项式混沌系统并进行均匀化处理,对其产生的序列进行了信息熵、Kolmogorov熵和离散熵分析,结果显示该均匀化方法的均匀化效果显著且不改变序列混沌程度。
  • 图  1  统计直方图

    图  2  均匀化前后系统K熵与离散熵对比图

    表  1  几个2次多项式混沌系统

    混沌系统$f(x)$概率密度均匀化系统$z(x)$$f(x)$信息熵$z(x)$信息熵
    $f(x) = \frac{7}{2}{x^2} + \frac{{33}}{{10}}x - \frac{{53}}{{200}}$$\frac{7}{{{\text{π}} \sqrt { - 49{x^2} + 46.2x + 5.11} }}$$z(x) = \frac{1}{{\text{π}} }\arcsin \left( { - \frac{7}{4}x - \frac{{33}}{{40}}} \right)$8.64708.9651
    $f(x) = \frac{5}{4}{x^2} - \frac{1}{2}x - \frac{{27}}{{20}}$$\frac{5}{{{\text{π}} \sqrt { - 25{x^2} + 10x + 63} }}$$z(x) = \frac{1}{{\text{π}} }\arcsin\left( { - \frac{5}{8}x + \frac{1}{8}} \right)$8.63808.9649
    $f(x) = - \frac{5}{2}{x^2} + 3x + \frac{1}{2}$$\frac{5}{{{\text{π}} \sqrt { - 25{x^2} + 30x + 7} }}$$z(x) = \frac{1}{{\text{π}} }\arcsin\left( {\frac{5}{4}x - \frac{3}{4}} \right)$8.64128.9650
    下载: 导出CSV

    表  2  系统均匀化前后的信息熵与最大熵比较

    $\left( {N,M} \right)$均匀化前
    信息熵
    均匀化后
    信息熵
    最大熵
    (500000, 100)6.35306.64376.6439
    (500000, 300)7.91378.22848.2288
    (500000, 500)8.64318.96518.9658
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-07-19
  • 修回日期:  2019-01-17
  • 网络出版日期:  2019-02-14
  • 刊出日期:  2019-07-01

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