关于G-P算法计算混沌关联维的讨论

G-P algorithm for evaluating the correlation dimension in chaos

关联维是描述混沌系统的一个重要的特征不变量,而G-P算法是目前计算关联维数的一个主要的算法,但是在使用G-P算法时,由于许多参量的选取存在很大的主观性,不同的选取会得到不同的结果,这个问题以前一直没有得到较好的解决。以具有解析结果Lorenz系统进行实例分析,指出采用G-P算法计算关联维数时,应对相关参数进行慎重和细致的选取,否则得出的结论将缺乏说服力。研究结果表明,不同的范数选取对关联维的计算影响很小、时间序列数据量大小的选取应以能够获得稳定的分数维为准则、重构相空间嵌入维数不能随意指定,但也不是越大越好,对Lorenz系统而言最大取到10较为合适。

The correlation dimension is an important invariant for chaotic system, and G-P algorithm is the main way to calculate the correlation dimension. There are many different results caused by the subjectivity in the choosing of parameters, and different parameter choice will get different results. In this paper, based on the Lorenz equation which has analytical result, it is pointed out that the choosing of parameters need circumspection in the calculating of the correlation dimension by Grassberger-Procaccia （G-P） algorithm. For Lorenz system time series, the calcu-lating results show that the influence on the correlation dimension for different norms choice is small, that the best sampling number is the number that can gets the steady fractal characteristic, that the embedding dimension of the phase space is not appointed at random nor the bigger the better, and that the maximal embedding dimension of the phase space is 10 for Lorenz system.