计算机应用 ›› 2019, Vol. 39 ›› Issue (10): 2997-3001.DOI: 10.11772/j.issn.1001-9081.2019020255

• 先进计算 • 上一篇    下一篇

基于均匀化分布的Chebyshev映射系统构建及特性分析

黄滨, 保利勇, 丁洪伟   

  1. 云南大学 信息学院, 昆明 650500
  • 收稿日期:2019-02-14 修回日期:2019-05-08 出版日期:2019-10-10 发布日期:2019-05-14
  • 通讯作者: 保利勇
  • 作者简介:黄滨(1990-),男,广东汕头人,硕士研究生,主要研究方向:混沌理论与控制、非线性科学、优化算法;保利勇(1975-),男,云南楚雄人,副教授,博士,主要研究方向:计算机通信网、混沌扩频通信、网络安全;丁洪伟(1964-),男,云南昆明人,教授,博士生导师,博士,主要研究方向:轮询、通信网络理论与控制协议。
  • 基金资助:
    国家自然科学基金资助项目(61461053)。

Construction and characteristic analysis of Chebyshev mapping system based on homogenized distribution

HUANG Bin, BAO Liyong, DING Hongwei   

  1. Information School, Yunnan University, Kunming Yunnan 650500, China
  • Received:2019-02-14 Revised:2019-05-08 Online:2019-10-10 Published:2019-05-14
  • Supported by:
    This work is partially supported by the National Natural Science Foundation of China (61461053).

摘要: 针对传统Chebyshev映射所呈现的值域边界双峰的分布特性,为满足优化理论中序列均匀分布的需求,结合Chebyshev映射概率密度函数进行数理推导,将得到的随机变量函数与原映射级复合成新的系统。通过对比研究表明,系统具有良好的均匀分布特性、遍历特性、平衡性和较低的复杂度,所产生序列的随机误差小,相似度高。最后将系统应用于优化算法中的初始化种群阶段,进一步说明了所做的均匀化分布系统在改善原序列均匀分布特性的效果是显著的。

关键词: 混沌, 动力学系统, Chebyshev映射, 均匀化分布, 混沌特性

Abstract: Concerning the bimodal distribution characteristics of the range boundary presented by the traditional Chebyshev mapping, in order to meet the requirements of homogenized distribution of sequences in optimization theory, the mathematical equation was given by using the probability density function of Chebyshev mapping, and a new system was constructed by combining with the original mapping into a new system. The comparative study shows that the system has good homogenized distribution characteristic, ergodic characteristic, balance and low complexity, and the random error of the generated sequences is small and the similarity is high. Finally, the system is applied to the initialization population stage of the optimization algorithm, and it is further shown that the homogenized distribution system has a significant effect on improving the homogenized distribution characteristic of the original mapping.

Key words: chaos, dynamics system, Chebyshev mapping, homogeneous distribution, chaotic characteristic

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