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Determining Lyapunov exponents from a time series

Department of Physics, University of Texas, Austin, Texas 78712, USA
Physica D Nonlinear Phenomena (Impact Factor: 1.83). 07/1985; DOI: 10.1016/0167-2789(85)90011-9

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.

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