Characterization of spatiotemporal chaos from time series

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Abstract
The analysis of time series generated by spatiotemporal chaotic systems is discussed. We find that a Grassberger-Procaccia algorithm with a suitable normalization for the correction of systematic errors caused by the shape of the attractor is a reliable method for distinguishing between high-dimensional chaos and noise. We show that even a quantitative description of the attractor is possible by means of dimension densities. The results obtained from the time series are in good agreement with values calculated directly from the generating equations of motion.