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Zbl 0585.58037
Wolf, Alan; Swift, Jack B.; Swinney, Harry L.; Vastano, John A.
Determining Lyapunov exponents from a time series. (English)
[J] Physica D 16, 285-317 (1985). ISSN 0167-2789

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."
[K.Furutani]

MSC 2000:: *37-99 Dynamic systems and ergodic theory

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

Cited in: Zbl 1236.74233 Zbl 1212.37059 Zbl 1175.65146 Zbl 0906.65082 Zbl 0732.62090

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