00-158 R. Carretero-Gonzalez, S. Orstavik and J. Stark

Quasi-diagonal reconstruction of Lyapunov spectra for spatio-temporal systems from multivariate time series (278K, LaTeX with PS figures) Apr 4, 00

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Abstract. We use multivariate time-series generated by spatially extended systems to reconstruct their entire Lyapunov spectrum. Provided short range, or exponentially decaying, spatial interactions it is possible to approximately reconstruct the Jacobian by a banded matrix. Thus, by applying spatially localised reconstructions of the tangent space we estimate the whole Jacobian. This method circumvents the ``curse of dimensionality'' when trying to spatio-temporally embed the high-dimensional dynamics for extended dynamical systems. The technique is illustrated using coupled map lattices as prototype models for spatio-temporal chaos.

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