THE INFLUENCE OF NOISE ON THE CORRELATION DIMENSION OF CHAOTIC ATTRACTORS

The present paper investigates the influence of noise on the correlati on dimension D-e of chaotic attractors arising in discrete and continu ous in time dynamical systems. Our numerical results indicate that the presence of noise leads to an increase of the correlation dimension. Assuming that the correlation dimension for a white noise is infinite, we prove, first, that the increase of the dimension of a chaotic attr actor in a stochastic system is a generic property of the set of stoch astic dynamical systems and, secondly, that the existence of a small c orrelation dimension in a rime series implies that the deterministic p art of its Wold decomposition is nonzero. We also present a collection of dynamical systems subject to noise which may he considered as mode ls for predictions on the response of time series with a finite correl ation dimension, as encountered in physical or numerical experiments. (C) 1998 Elsevier Science Ltd. All rights reserved.