ESTIMATING THE DIMENSION OF HIGH-DIMENSIONAL ATTRACTORS - A COMPARISON BETWEEN 2 ALGORITHMS

We compare two algorithms for the numerical estimation of the correlat ion dimension from a finite set of vectors: the ''classical'' algorith m of Grassberger and Procaccia (GPA) and the recently proposed algorit hm of Judd (JA). Data set size requirements and their relations to sys tematic and statistical errors of the estimates are investigated. It i s demonstrated that correlation dimensions of the order of 6 can corre ctly be resolved on the basis of about 100 000 data points in the case of a continuous trajectory on a strange attractor; the minimum data s et size is, however, noticeably dependent on the geometrical structure of the system from which the vectors were sampled. (C) 1998 Elsevier Science B.V. All rights reserved.