Abstract
DETERMINING whether time series of data from dynamical systems exhibit regular, stochastic or chaotic behaviour is a goal in a wide variety of problems. For sparse time series (those containing only of the order of 1,000 data points), the goal may simply be to discover whether the series are chaotic or not. Examples are case rates for infectious diseases1 and proxy palaeoclimatic records from deep-sea cores2. Sugihara and May3 have recently extended previous work4 aimed at distinguishing chaos from noise in sparse time series. Their approach is based on a comparison of future predictions of terms in the time series—derived using a data base of information from another part of the series—with the known terms. Here I present a method for estimating from such forecasting the largest Liapunov exponent of the dynamics, which provides a measure of how chaotic the system is—that is, how rapidly information is lost from the system.
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References
Olsen, L. F. & Schaffer, W. M. Science 249, 499–504 (1990).
Nicolis, C. & Nicolis, G. Nature 311, 529–532 (1984).
Sugihara, G. & May, M. Nature 344, 734–741 (1990).
Farmer, J. D. & Sidorowich, J. J. Phys. Rev. Lett. 59, 845–848 (1987).
Kolmogorov, A. N. Dokl. Acad. SSSR 124, 754 (1959).
Mandelbrot, B. B. The Fractal Geometry of Nature (Freeman, New York, 1983).
Schuster, H. G. Deterministic Chaos 2nd Ed. (VCH, Weinheim, 1989).
Grassberger, P. & Procaccia, I., Phys. Rev. A28, 2591–2593 (1983).
Grassberger, P. Nature 323, 609–612 (1986).
Vautard, R. & Ghil, M. Physica D35, 395–424 (1989).
Shannon, C. & Weaver, W. The Mathematical Theory of Communication (Illinois University Press, Urbana, 1949).
Schlögl, F. Probability and Heat (Vieweg, Braunschweig, 1989).
Sano, M. & Sawada, Y. Phys. Rev. Lett. 55, 1082–1085 (1985).
Eckmann, J.-P., Kamphorst, S. O., Ruelle, D. & Ciliberto, S. Phys. Rev. A34, 4971–4979 (1986).
Lichtenburg, A. J. & Lieberman, M. A. Regular and Stochastic Motion (Springer, New York, 1983).
Beck, T. L., Leitner, D. M. & Berry, R. S. J. chem. Phys. 89, 1681–1694 (1988).
Casdagli, M. Physica D35, 335–356 (1989).
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Wales, D. Calculating the rate of loss of information from chaotic time series by forecasting. Nature 350, 485–488 (1991). https://doi.org/10.1038/350485a0
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DOI: https://doi.org/10.1038/350485a0
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