# 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 Stemler^{1,2}, •Johannes P. Werner^{1}, Hartmut Benner^{1}, and Wolfram Just^{3} — ^{1}Institut für Festkörperphysik, TU Darmstadt, 64289 Darmstadt — ^{2}School of Mathematics and Statistics, University of Western Australia, Crawley WA 6009, Australia — ^{3}Queen 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)