Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 30: Nonlinear stochastic systems
DY 30.3: Vortrag
Freitag, 29. Februar 2008, 10:45–11:00, MA 001
Stochastic modelling of experimental chaotic time series — Thomas Stemler1,2, •Johannes P. Werner1, Hartmut Benner1, and Wolfram Just3 — 1Institut für Festkörperphysik, TU Darmstadt, 64289 Darmstadt — 2School of Mathematics and Statistics, University of Western Australia, Crawley WA 6009, Australia — 3Queen Mary / University of London, School of Mathematical Sciences, London E1 4NS, UK
Modelling dynamical degrees of freedom by suitable stochastic forces is a classical subject in theoretical physics and applied mathematics. While the replacement of many degrees of freedom in a thermodynamic system by Gaussian white noise is a textbook example and the foundation of e.g. irreversible thermodynamics, it is quite a recent finding that even few chaotic degrees of freedom can be modelled by stochastic differential equations.
Applying the Kramers–Moyal expansion to data from an electronic circuit experiment, we obtain a stochastic model of the low dimensional chaotic system [1]. We demonstrate that reliable drift and diffusion coefficients can be obtained even when there is no pronounced time scale separation. By comparing the analytical solution of the corresponding Fokker–Planck equation with experimental data we show that crisis induced intermittency can be described in terms of a stochastic model which is dominated by state space dependent diffusion.
[1] Phys.Rev.Lett. 98 No. 4, 044102 (2007)