Abstract
An approach is presented for making short-term predictions about the trajectories of chaotic dynamical systems. The method is applied to data on measles, chickenpox, and marine phytoplankton populations, to show how apparent noise associated with deterministic chaos can be distinguished from sampling error and other sources of externally induced environmental noise.
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References
Lorenz, E. N. J. atmos. Sci. 26, 636–646 (1969).
Tong, H. & Lim, K. S. Jl. R. statist. Soc. 42, 245–292 (1980).
Farmer, J. D. & Sidorowich, J. J. Phys. Rev. Lett. 62, 845–848 (1987).
Priestly, M. B. J. Time Series Analysis 1, 47–71 (1980).
Eckman, J. P. & Ruell, D. Rev. mod. Phys. 57, 617–619 (1985).
Crutchfield, J. P. & MacNamara, B. S. Complex Systems 1, 417–452 (1987).
Casdagli, M. Physics D, 35, 335–356 (1989).
Grassberger, P. & Procaccia, I. Phys. Rev. Lett. 50, 346–369 (1983).
Schwartz, I. J. math. Biol. 21, 347–361 (1985).
Schaffer, W. M. & Kot, M. J. theor. Biol. 112, 403–407 (1985).
Schaffer, W. M. & Kot, M. in Chaos: An introduction (ed. Holden, A. V.) (Princeton Univ. Press, 1986).
Schaffer, W. M., Ellner, S. & Kot, M. J. math. Biol. 24, 479–523 (1986).
Schaffer, W. M., Olsen, L. F., Truty, G. L., Fulmer, S. L. & Graser, D. J. in From Chemical to Biological Organization (eds Markus, M., Muller, S. C. & Nicolis, G.) (Springer-Verlag, New York, 1988).
Yule, G. U. Phil. Trans. R. Soc. A226, 267–278 (1927).
Takens, F. in Dynamical Systems and Turbulence (Springer-Verlag, Berlin, 1981).
Farmer, J. D. & Sidorowich, J. J. in Evolution, Learning and Cognition (ed. Lee, Y. C.) (World Scientific, New York, 1989).
London, W. P. & Yorke, J. A. Am. J. Epidem. 98, 453 (1973).
Pimm, S. L. & Redfearn, A. Nature 334, 613–614 (1988).
Lawton, J. H. Nature 334, 563 (1988).
Helsenstein, U. Statist. Med. 5, 37–47 (1986).
Anderson, R. M. & May, R. M. Nature 318, 323–329 (1985).
Anderson, R. M., Grenfell, B. T. & May, R. M. J. Hyg. 93, 587–608 (1984).
Tont, S. A. J. mar. Res. 39, 191–201 (1981).
Varosi, F., Grebogi, C. & Yorke, J. A. Phys. Lett. A124, 59–64 (1987).
Abarbanel, H. D., Kadtke, J. B. & Brown, R. Phys. Rev. B41, 1782–1807 (1990).
Mees, A. I. Research Report No. 8 (Dept Mathematics, University of Western Australia, 1989).
Drepper, F. R. in Erodynamics (eds Wolff, W., Soeder, C. J. & Drepper, F. R.) (Springer-Verlag, New York, 1988).
Ruelle, D. Proc. R. Soc. A (in the press).
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Sugihara, G., May, R. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344, 734–741 (1990). https://doi.org/10.1038/344734a0
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