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Determining Lyapunov Exponents from a Time Series (1985)
| Venue: | Physica |
| Citations: | 495 - 1 self |
BibTeX
@ARTICLE{Wolf85determininglyapunov,
author = {Alan Wolf and Jack B. Swift and Harry L. Swinney and John A. Vastano},
title = {Determining Lyapunov Exponents from a Time Series},
journal = {Physica},
year = {1985},
pages = {285--317}
}
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Abstract
We present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of nearby orbits in phase space. A system with one or more positive Lyapunov exponents is defined to be chaotic. Our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems: we monitor the long-term growth rate of small volume elements in an attractor. The method is tested on model systems with known Lyapunov spectra, and applied to data for the Belousov-Zhabotinskii reaction and Couette-Taylor flow. Contents 1.
Keyphrases
lyapunov exponent time series long-term growth rate defined model system positive lyapunov exponent fast divergence dynamical behavior non-negative lyapunov exponent belousov-zhabotinskii reaction quantitative characterization small volume element couette-taylor flow known lyapunov spectrum experimental time series first algorithm phase space nearby orbit model system
