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Detection of nonlinear dynamics in short, noisy time series

Nature volume 381, pages 215–217 (1996)Cite this article

Abstract

THE accurate identification of deterministic dynamics in an experimentally obtained time series1–5 can lead to new insights regarding underlying physical processes, or enable prediction, at least on short timescales. But deterministic chaos arising from a nonlinear dynamical system can easily be mistaken for random noise6–8. Available methods to distinguish deterministic chaos from noise can be quite effective, but their performance depends on the availability of long data sets, and is severely degraded by measurement noise. Moreover, such methods are often incapable of detecting chaos in the presence of strong periodicity, which tends to hide underlying fractal structures9. Here we present a computational procedure, based on a comparison of the prediction power of linear and nonlinear models of the Volterra–Wiener form10, which is capable of robust and highly sensitive statistical detection of deterministic dynamics, including chaotic dynamics, in experimental time series. This method is superior to other techniques1–6,11,12 when applied to short time series, either continuous or discrete, even when heavily contaminated with noise, or in the presence of strong periodicity.

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Author information

Author notes

  1. Chi-Sang Poon: To whom correspondence should be addressed.

Authors and Affiliations

  1. Physics Department, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts, 02139, USA

    Mauricio Barahona

  2. Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts, 02139, USA

    Chi-Sang Poon

Authors
  1. Mauricio Barahona
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  2. Chi-Sang Poon
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Barahona, M., Poon, CS. Detection of nonlinear dynamics in short, noisy time series. Nature 381, 215–217 (1996). https://doi.org/10.1038/381215a0

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