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DY: Fachverband Dynamik und Statistische Physik

DY 60: Poster - complex systems and data analysis

DY 60.3: Poster

Thursday, March 19, 2015, 16:00–18:00, Poster A

(How) Can we trust in Lyapunov exponents estimated from time series? — •Ulrich Parlitz — Max Planck Institute for Dynamics and Selforganization, Göttingen, Germany — Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Germany

Lyapunov exponents are fundamental for quantifying sensitive dependence on initial conditions and chaos. While their computation using dynamical evolution equations is quite straight forward (even for high dimensions and extended systems) estimating Lyapunov exponents from time series remains a challenge. We shall discuss and illustrate problems and pitfalls using time series generated by different chaotic systems. In particular we shall consider a six dimensional Lorenz-96 model that possesses a chaotic attractor (Kaplan-Yorke dimension D=4.18) with a single positive Lyapunov exponent. For this example estimation of the (largest) Lyapunov exponent(s) turns to be quite difficult and requires very long time series indicating practical limits of purely data based estimation methods.