Distortions of reconstruction for chaotic attractors

✍ Scribed by Alexei Potapov

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 949 KB
• Volume: 101
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(96)00234-5

✦ Synopsis

We consider the problem of quality evaluation for delay reconstruction of chaotic attractors from scalar time series. The proposed approach is based upon local linear analysis of the reconstruction mapping. It is shown that some linear distortions in principle could be corrected, but usually nonlinear distortions make it difficult to efficiently apply this technique. The new algorithms of estimating the scale of nonlinear distortion and "irrelevance time" (upper limit for the reconstruction window) from a time series are proposed. Both of them do not require precise knowledge of minimal embedding dimension for the attractor studied.