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Wolf, Alan; Swift, Jack B.; Swinney, Harry L.; Vastano, John A.

Determining Lyapunov exponents from a time series. (English) Zbl 0585.58037

Physica D 16, 285-317 (1985).
Authors’ summary: ”We present the first algorithms that allow the estimation of nonnegative 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-Zhabotinskij reaction and Couette-Taylor flow.”
Reviewer: K.Furutani

Cited in 5 Reviews
Cited in 1237 Documents

MSC:

37-XX Dynamical systems and ergodic theory

Keywords:

Lyapunov spectra; chaos; dynamical system; Lyapunov exponents; dynamical behavior; attractor

Software:

Lyapunov Exponents for ODE
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\textit{A. Wolf} et al., Physica D 16, 285--317 (1985; Zbl 0585.58037)
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References:

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