韦心元,
袁悦
北京科技大学数理学院 北京 100083
基金项目:中央高校基本科研业务费专项资金(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同步理论与混沌密码学
韦心元：男，1994年生，硕士生，研究方向为混沌系统理论与混沌密码学
袁悦：女，1996年生，硕士生，研究方向为混沌系统理论与混沌密码学
通讯作者:臧鸿雁 zhylixiang@126.com
中图分类号:TN918.1计量
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被引次数:0
出版历程
收稿日期:2019-11-04
修回日期:2020-03-12
网络出版日期:2020-12-11
刊出日期:2021-02-23
Determination and Properties Analysis of a Cubic Polynomial Chaotic Map
Hongyan ZANG,,Xinyuan WEI,
Yue YUAN
Mathematics and Physics School, University of Science and Technology Beijing, Beijing 100083, China
Funds:The Fundamental Research Funds for the Central Universities of Ministry of Education of China (06108236)
摘要
摘要:该文给出了一般3次多项式映射与分段线性混沌映射拓扑共轭的充分条件，从而间接地给出了一般3次多项式成为混沌系统的充分条件。进一步对拓扑共轭的分段线性映射和多项式映射的均匀性、结构复杂性和随机性进行了分析，结果显示分段线性映射的均匀性优于多项式映射，多项式映射的随机性优于分段线性映射，在结构复杂性方面，二者没有显著差异，但量化方法对二者的结构复杂性影响显著。
关键词:混沌系统/
多项式映射/
拓扑共轭/
复杂性/
随机性
Abstract:This paper provides the sufficient conditions for topological conjugation between the general cubic polynomial maps and a piecewise linear chaotic map, then provides indirectly the sufficient conditions that make the cubic polynomial maps be chaotic. This paper analyzes further the uniformity, structural complexity and randomness of the piecewise linear map and cubic polynomial maps of topological conjugation. The results show that the uniformity of the piecewise linear map is better than the polynomial maps while the randomness of the polynomial maps is superior to the piecewise linear map. As for the structural complexity, there is no significant difference between the two kinds of systems, but it should be noted that the quantitative method makes a significant impact on the structure complexity of the systems.
Key words:Chaotic system/
Polynomial maps/
Topological conjugation/
Complexity/
Randomness
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