Reconstruction of systems with delayed feedback: II. Application

Year: 2000

Authors: Bunner M.J., Ciofini M., Giaquinta A., Hegger R., Kantz H., Meucci R., Politi A.

Autors Affiliation: Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy;
Max Planck Institut fur Physik Komplexer Systeme, Nothnitzer Str. 38, 01187 Dresden, Germany;
INFM, Unità di Firenze, 50125 Firenze Italy

Abstract: We apply a recently proposed method for the analysis of time series from systems with delayed feedback to experimental data generated by a CO2 laser. The method allows estimating the delay time with an error of the order of the sampling interval, while an approach based on the peaks of either the autocorrelation function, or the time delayed mutual information would yield systematically larger values. We reconstruct rather accurately the equations of motion and, in turn, estimate the Lyapunov spectrum even for high dimensional attractors. By comparing models constructed for different \”embedding dimensions\” with the original data, we are able to find the minimal faithful model. For short delays, the results of our procedure have been cross-checked using a conventional Takens time-delay embedding. For large delays, the standard analysis is inapplicable since the dynamics becomes hyperchaotic. In such a regime we provide the first experimental evidence that the Lyapunov spectrum, rescaled according to the delay time, is independent of the delay time itself. This is in full analogy with the independence of the system size found in spatially extended systems.

Journal/Review: EUROPEAN PHYSICAL JOURNAL D

Volume: 10 (2)      Pages from: 177  to: 187

KeyWords: Time-series; Attractors
DOI: 10.1007/s100530050539

Citations: 28
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