7 research outputs found
A quasi-diagonal approach to the estimation of Lyapunov spectra for spatio-temporal systems from multivariate time series
We describe methods of estimating the entire Lyapunov spectrum of a spatially
extended system from multivariate time-series observations. Provided that the
coupling in the system is short range, the Jacobian has a banded structure and
can be estimated using spatially localised reconstructions in low embedding
dimensions. This circumvents the ``curse of dimensionality'' that prevents the
accurate reconstruction of high-dimensional dynamics from observed time series.
The technique is illustrated using coupled map lattices as prototype models for
spatio-temporal chaos and is found to work even when the coupling is not
strictly local but only exponentially decaying.Comment: 13 pages, LaTeX (RevTeX), 13 Postscript figs, to be submitted to
Phys.Rev.
Estimation of Delay Times From a Delayed Optical Feedback Laser Experiment
. -- We estimate delay times from high-dimensional chaotic time series experimentally obtained from a fast optical time-delayed feedback system. The experiment consists of a semiconductor laser, where the instabilities are induced by an external T-shaped cavity introducing two delay times into the laser. The delay times are determined by a filling factor analysis and found to give a better estimate than those obtained by autocorrelation functions. Finally, the possibility of this method for the reconstruction of the system's di#erential equations is discussed. The characterization of nonlinear dynamical behavior and the identification of the underlying deterministic time-evolution laws from experimental time series has turned out to be one of the key problems in the study of nonlinear dynamical systems. For dynamical systems with a low number of degrees of freedom, embedding techniques [1] have been exceptionally successful for the computation of chaotic indicators (dimensions, Lyapun..