混沌的复杂度研究方法和Logistic映射分析  

STUDY ON THE CHAOS' COMPLEXITY ANALYSIS METHODOLOGY AND APPLICATION TO LOGISTIC MAP

作　　者：王云雄[1] 翁贻方[1] 郑德玲[2] 

机构地区：[1]北京工商大学信息工程学院,北京100037 [2]北京科技大学信息工程学院,北京100083

出　　处：《北京工商大学学报（自然科学版）》2006年第2期38-41,共4页Journal of Beijing Technology and Business University:Natural Science Edition

基　　金：北京市优秀人才培养专项经费资助项目(20041D0500309)

摘　　要：研究和评价了混沌复杂度3种定量分析方法——Lyapunov指数、分维、测度熵,及其它们之间的内在联系,并研究了一种简单有效的测度熵替代方法——近似熵(approx im ate entropy)方法.应用以上方法对Log istic映射复杂度进行了分析.结果表明Lyapunov指数和测度熵的值与复杂度基本呈线性关系,分维数与复杂度的函数关系尚难确定,且与Lyapunov指数、测度熵之间的关系也不明确.Three kinds of chaos＇ complexity analysis methods ,Lyapunov exponent, fractai and K- S entropy, as well as their relationship, are investigated. Approximate entropy （ApEn） method is also studied. They are applied to analyze the complexity of Logistic map. The conclusion is that Lyapunov exponent and K-S entropy have approximately linear relation with complexity, while it is difficult to determine the relation between fractal and complexity. Furthermore the correlation of fractal and Lyapunov exponent, K-S entropy is not clear now. Finally, ApEn method offers a simple and valid analysis mean to substitute K-S entropy.

关 键 词：混沌 复杂度 LYAPUNOV指数 分维 测度熵 

分 类 号：TP301.5[自动化与计算机技术—计算机系统结构] N941.4[自动化与计算机技术—计算机科学与技术]