Measurement of the Lyapunov spectrum from a chaotic time series

Details Measurement of the Lyapunov spectrum from a chaotic time series Measurement of the Lyapunov spectrum from a chaotic time series

Sep 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985phrvl..55.1082s&link_type=abstract

Physical Review Letters (ISSN 0031-9007), vol. 55, Sept. 2, 1985, p. 1082-1085.

Mathematics

Dynamical Systems

200

Chaos, Dynamical Systems, Liapunov Functions, Nonlinear Systems, Rayleigh-Benard Convection, Entropy, Exponents, Fractals, Rayleigh Number, Water

Scientific paper

The exponential divergence or convergence of nearby trajectories (Liapunov exponents) is conceptually the most basic indicator of deterministic chaos. A new method is proposed to determine the spectrum of several Liapunov exponents (including positive, zero, and even negative ones) from the observed time series of a single variable. The method has been applied to various known model systems and also to the Rayleigh-Benard experiment, and the dependence of the Liapunov exponents on the Rayleigh number has been elucidated.

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