## Determining Lyapunov Exponents from a Time Series (1985)

Venue: | Physica |

Citations: | 230 - 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}

}

### Years of Citing Articles

### OpenURL

### 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.