Estimation of the dimension of a noisy attractor

Abstract

A simple method is proposed to estimate the correlation dimension of a noisy chaotic attractor. The method is based on the observation that the noise induces a bias in the observed distances of trajectories, which tend to appear farther apart than they are. Under the assumption of noise being strictly bounded in amplitude, this leads to a rescaling of interpoint distances on the attractor. A correlation integral function is obtained that accounts for this effect of noise. The applicability of the method is illustrated with two examples, viz., the Lorenz attractor with additive noise and experimental time series of pressure fluctuation data measured in gas-solid fluidized beds.