Determining Lyapunov exponents from a time series

Alan Wolf (1) , Jack Swift (1) , Harry L. Swinney (1) , John Vastano (1)

1 University of Texas at Austin [Austin]

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.

Domaines: Mécanique des structures [physics.class-ph]

Alan Wolf, Jack Swift, Harry L. Swinney, John Vastano. Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 1985, 16 (3), pp.285 - 317. ⟨10.1016/0167-2789(85)90011-9⟩. ⟨hal-01654059⟩