Measuring the strangeness of strange attractors
Abstract
We study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise. The exponent v is closely related to the fractal dimension and the information dimension, but its computation is considerably easier. Its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed. Algorithms for extracting v from the time series of a single variable are proposed. The relations between the various measures of strange attractors and between them and the Lyapunov exponents are discussed. It is shown that the conjecture of Kaplan and Yorke for the dimension gives an upper bound for v. Various examples of finite and infinite dimensional systems are treated, both numerically and analytically.
 Publication:

Physica D Nonlinear Phenomena
 Pub Date:
 October 1983
 DOI:
 10.1016/01672789(83)902981
 Bibcode:
 1983PhyD....9..189G