Finding Chaos in Noisy Systems
SUMMARY In the past 20 years there has been much interest in the physical and biological sciences in non‐linear dynamical systems that appear to have random, unpredictable behaviour. One important parameter of a dynamical system is the dominant Lyapunov exponent (LE). When the behaviour of the syste...
Published in: | Journal of the Royal Statistical Society: Series B (Methodological) |
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Oxford University Press (OUP)
1992
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croxfordunivpr:10.1111/j.2517-6161.1992.tb01889.x 2024-05-12T08:04:56+00:00 Finding Chaos in Noisy Systems Nychka, Douglas Ellner, Stephen Gallant, A. Ronald McCaffrey, Daniel 1992 http://dx.doi.org/10.1111/j.2517-6161.1992.tb01889.x https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fj.2517-6161.1992.tb01889.x https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1992.tb01889.x en eng Oxford University Press (OUP) http://onlinelibrary.wiley.com/termsAndConditions#vor Journal of the Royal Statistical Society: Series B (Methodological) volume 54, issue 2, page 399-426 ISSN 0035-9246 2517-6161 Statistics and Probability journal-article 1992 croxfordunivpr https://doi.org/10.1111/j.2517-6161.1992.tb01889.x 2024-04-18T08:18:00Z SUMMARY In the past 20 years there has been much interest in the physical and biological sciences in non‐linear dynamical systems that appear to have random, unpredictable behaviour. One important parameter of a dynamical system is the dominant Lyapunov exponent (LE). When the behaviour of the system is compared for two similar initial conditions, this exponent is related to the rate at which the subsequent trajectories diverge. A bounded system with a positive LE is one operational definition of chaotic behaviour. Most methods for determining the LE have assumed thousands of observations generated from carefully controlled physical experiments. Less attention has been given to estimating the LE for biological and economic systems that are subjected to random perturbations and observed over a limited amount of time. Using nonparametric regression techniques (neural networks and thin plate splines) it is possible to estimate the LE consistently. The properties of these methods have been studied with simulated data and are applied to a biological time series: marten fur returns for the Hudson Bay Company (1820–1900). On the basis of a nonparametric analysis there is little evidence for low dimensional chaos in these data. Although these methods appear to work well for systems perturbed by small amounts of noise, finding chaos in a system with a significant stochastic component may be difficult. Article in Journal/Newspaper Hudson Bay Oxford University Press Hudson Hudson Bay Journal of the Royal Statistical Society: Series B (Methodological) 54 2 399 426 |
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Open Polar |
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Oxford University Press |
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croxfordunivpr |
language |
English |
topic |
Statistics and Probability |
spellingShingle |
Statistics and Probability Nychka, Douglas Ellner, Stephen Gallant, A. Ronald McCaffrey, Daniel Finding Chaos in Noisy Systems |
topic_facet |
Statistics and Probability |
description |
SUMMARY In the past 20 years there has been much interest in the physical and biological sciences in non‐linear dynamical systems that appear to have random, unpredictable behaviour. One important parameter of a dynamical system is the dominant Lyapunov exponent (LE). When the behaviour of the system is compared for two similar initial conditions, this exponent is related to the rate at which the subsequent trajectories diverge. A bounded system with a positive LE is one operational definition of chaotic behaviour. Most methods for determining the LE have assumed thousands of observations generated from carefully controlled physical experiments. Less attention has been given to estimating the LE for biological and economic systems that are subjected to random perturbations and observed over a limited amount of time. Using nonparametric regression techniques (neural networks and thin plate splines) it is possible to estimate the LE consistently. The properties of these methods have been studied with simulated data and are applied to a biological time series: marten fur returns for the Hudson Bay Company (1820–1900). On the basis of a nonparametric analysis there is little evidence for low dimensional chaos in these data. Although these methods appear to work well for systems perturbed by small amounts of noise, finding chaos in a system with a significant stochastic component may be difficult. |
format |
Article in Journal/Newspaper |
author |
Nychka, Douglas Ellner, Stephen Gallant, A. Ronald McCaffrey, Daniel |
author_facet |
Nychka, Douglas Ellner, Stephen Gallant, A. Ronald McCaffrey, Daniel |
author_sort |
Nychka, Douglas |
title |
Finding Chaos in Noisy Systems |
title_short |
Finding Chaos in Noisy Systems |
title_full |
Finding Chaos in Noisy Systems |
title_fullStr |
Finding Chaos in Noisy Systems |
title_full_unstemmed |
Finding Chaos in Noisy Systems |
title_sort |
finding chaos in noisy systems |
publisher |
Oxford University Press (OUP) |
publishDate |
1992 |
url |
http://dx.doi.org/10.1111/j.2517-6161.1992.tb01889.x https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fj.2517-6161.1992.tb01889.x https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1992.tb01889.x |
geographic |
Hudson Hudson Bay |
geographic_facet |
Hudson Hudson Bay |
genre |
Hudson Bay |
genre_facet |
Hudson Bay |
op_source |
Journal of the Royal Statistical Society: Series B (Methodological) volume 54, issue 2, page 399-426 ISSN 0035-9246 2517-6161 |
op_rights |
http://onlinelibrary.wiley.com/termsAndConditions#vor |
op_doi |
https://doi.org/10.1111/j.2517-6161.1992.tb01889.x |
container_title |
Journal of the Royal Statistical Society: Series B (Methodological) |
container_volume |
54 |
container_issue |
2 |
container_start_page |
399 |
op_container_end_page |
426 |
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1798847198113300480 |