Global scaling properties of a chaotic attractor reconstructed from experimental data

Abstract

Several aspects of attractor reconstruction and analysis using the method of correlation integrals have been thoroughly investigated for a specific chaotic attractor. Requirements on the experimental data, the generation of the artificial phase space, and the evaluation of the correlation integral are considered in detail. In order to explain the surprisingly smooth behavior of the correlation integrals resulting in an unusually straightforward and accurate analysis, the global scaling properties of the attractor are derived. They indicate that specific aspects of the analysis are a direct consequence of the structure of the attractor. Moreover, the scaling properties provide a useful criterion for an optimum adaption of the length of the required time series to the particular attractor under consideration.