Jc. Schouten et al., ESTIMATION OF THE DIMENSION OF A NOISY ATTRACTOR, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(3), 1994, pp. 1851-1861
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, wh
ich tend to appear farther apart than they are. Under the assumption o
f noise being strictly bounded in amplitude, this leads to a rescaling
of interpoint distances on the attractor. A correlation integral func
tion is obtained that accounts for this effect of noise. The applicabi
lity 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.