Abstract
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.
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