Quality of Delay Reconstruction for Chaotic Attractors and Choice of Reconstruction Parameters

We consider the problem of quality evaluation for delay reconstruction of chaotic attractors from scalar time series. The approach based upon local linear analysis of the reconstruction mapping is proposed. It is shown that the relevance weighting proposed by Farmer and Sidorowich is the method to avoid linear distortions. Usually nonlinear distortions do not enable efficiently apply this technique. The new algorithms of estimating the scale of nonlinear distortion and predictability time from a time series are proposed. Both of them, like Grassberger- Procaccia algorithm, do nor require precise knowledge of minimal embedding dimension for the attractor studied.