Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2000-04-06
Phys. Rev. E 62, 5 (2000) 6429-6439
Nonlinear Sciences
Chaotic Dynamics
13 pages, LaTeX (RevTeX), 13 Postscript figs, to be submitted to Phys.Rev.E
Scientific paper
10.1103/PhysRevE.62.6429
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.
Carretero-González Ricardo
Stark Jan
Ørstavik S.
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