Physical Sciences and Mathematics Commons^™

Mutual Information, Strange Attractors, And The Optimal Estimation Of Dimension, J. M. Martinerie, Alfonso M. Albano, A. I. Mees, P. E. Rapp

Physics Faculty Research and Scholarship

It has been shown that the appropriate setting of data windows is crucial to a successful estimation of a time-series correlation dimension using the Grassberger-Procaccia algorithm [Physica 9D, 189 (1983); Phys. Rev. Lett. 50, 346 (1983)], and it has been proposed that the first minimum of the corresponding mutual-information function may be an appropriate window value. We have tested this hypothesis against data generated by the Rossler equations, the Lorenz equations, and a three-dimensional irrational torus. We conclude that mutual information is not consistently successful in identifying the optimal window.