Determining Lyapunov exponents from a time series

Alan Wolf, Jack B. Swift, Harry L. Swinney, John A. Vastano
1985 Physica D : Non-linear phenomena  
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
more » ... pplied 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.
doi:10.1016/0167-2789(85)90011-9 fatcat:lyhy7o5igfefxbeivjxppyit4i