Determining Lyapunov exponents from a time series

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.

Process stationarity and reliability of trunk postural stability

“…Detailed description of these methods is available in Wolf (Wolf et al 1985) and Rosenstein (Rosenstein et al 1993). …”

Density-dependent dispersal and relative dispersal affect the stability of predator–prey metacommunities

“…Computation of 10 the Lyapunov exponent in fast oscillating models like ours gives easily rise to an important 11 computational error accumulation. For the sake of numerical accuracy, the first Lyapunov 12 exponent was estimated on a Poincaré section of the orbit, as the exponential increase of 13 deviations from the iterations of the Poincaré map (Wolf et al 1985). In each simulation, we 14 computed the Poincaré section that intersects the trajectory orthogonally at the asymptotic 15 time t asympt .…”

Fractal features of structures of gas flow in selected gas stations of I order

“…[8], [12], [18], [32] oraz [38]) ma miejsce także w przypadku, gdy szereg czasowy ma charakter białego szumu. Autorzy zwracają uwagę, że pewne procedury mogą prowadzić do tzw.…”