评价奇怪吸引子分形特征的Grassberger-Procaccia算法  

Grassberger-Procaccia algorithm for evaluating the fractal characteristic of strange attractors

作　　者：王安良[1] 杨春信[1] 

机构地区：[1]北京航空航天大学飞行器设计与应用力学系,北京100083

出　　处：《物理学报》2002年第12期2719-2729,共11页Acta Physica Sinica

基　　金：国家自然科学基金 (批准号 :5 0 1760 0 3 )资助的课题~~

摘　　要：基于Lorenz,R ssler和H啨ｎｏｎ三种典型的奇怪吸引子 ,全面分析了Grassberger Procaccia(缩写G P)算法 ,详细讨论了采样数据量、延迟时间、重构相空间维数和线性区长度等参数对计算关联维数和Kolmogorov熵的影响 ,结果表明这些关键参数是相互关联的 .通过分析关联积分谱的变化趋势 ,发现延迟时间与重构相空间维数对连续动力系统和离散动力系统的作用效果是不同的 ,且选择最佳延迟时间对计算关联维数的意义不大 .指出了实际中应用GBased on the three general strange attractors generated by the Lorenz equation, the Rossler equation and the Henon map, the Grassberger-Procaccia algorithm is analyzed. For a finite time series, the sampling number, delay time, embedding dimension and the length of scaling region affect the precision of evaluating the correlation dimension D-2 and the 2nd-order Kolmogorov entropy K-2 by G-P algorithm. In the analysis of the trend of a correlation integral, the impression for a continuous dynamical system is different from that of a discrete dynamical system in delay time and embedding dimension. The criterion of delay time chosen by mutual information is unnecessary for calculating the correlation dimension D-2. The applicable conditions for G-P algorithm is also indicated.

关 键 词：评价 分形特征 奇怪吸引子 Grassberger-Procaccia算法 关联维数 Kolmogorov熵 混沌 

分 类 号：O415.5[理学—理论物理]