Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series

  title={Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series},
  author={George Sugihara and Robert M. May},
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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  • Abarbanel, Brown, Kadtke
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  • Physical review. A, Atomic, molecular, and optical physics
  • 1990
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  • I. Schwartz
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  • Journal of mathematical biology
  • 1985
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