Open AccessGrassberger-Procaccia algorithm for evaluating the fractal characteristic of strange attractors
Author(s) -
AnLiang Wang,
Yang Chun-Xin
Publication year - 2002
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.51.2719
Subject(s) - attractor , correlation dimension , correlation integral , dimension (graph theory) , embedding , lorenz system , fractal dimension , mathematics , scaling , algorithm , dynamical systems theory , series (stratigraphy) , hénon map , entropy (arrow of time) , statistical physics , fractal , chaotic , correlation , mathematical analysis , computer science , physics , pure mathematics , artificial intelligence , geometry , paleontology , quantum mechanics , biology
Based on the three general strange attractors generated by the Lorenz equation, the Rssler equation and the Hénon 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.