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Determining Lyapunov exponents from a time series

Wolf, Alan ; Swift, Jack ; Swinney, Harry L ; Vastano, John Legrand, Mathias (Editor)

Physica D: Nonlinear Phenomena, July 1985, Vol.16(3), pp.285-317 [Periódico revisado por pares]

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  • Título:
    Determining Lyapunov exponents from a time series
  • Autor: Wolf, Alan ; Swift, Jack ; Swinney, Harry L ; Vastano, John
  • Legrand, Mathias (Editor)
  • Assuntos: Engineering Sciences ; Mechanics ; Mechanics of the Structures ; Engineering ; Physics
  • É parte de: Physica D: Nonlinear Phenomena, July 1985, Vol.16(3), pp.285-317
  • Descrição: 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 ftow.
  • Idioma: Inglês

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