Berlin 2008 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 14: Statistical physics II (general)

DY 14.3: Talk

Tuesday, February 26, 2008, 14:45–15:00, MA 004

Estimating fixed points of complex dynamical systems - with an application to wind energy research — •Julia Gottschall and Joachim Peinke — Institut für Physik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg

We present a method to estimate the fixed points of complex dynamical systems and show its robustness against different sources of noise. Assuming that the considered process can be described by a Langevin or Fokker-Planck equation, Friedrich et al. [1] proposed some years ago a procedure how to reconstruct its deterministic and stochastic dynamics, separately, directly from the data. Recently, it has been investigated how the reconstruction is affected by measurement noise as well as by a finite sampling frequency of the data, and more or less complex corrections have been suggested [2].

We have studied the reconstruction of the deterministic dynamics and the influence of the proposed corrections in more detail. In particular, we could show that a reliable estimation of the characteristic points is still possible with the uncorrected procedure, even when the system is spoilt by different kinds of noise. Therewith, we have a very efficient method to estimate the fixed points of a complex system.

This conclusion allows to apply the method to a variety of fields of interest. We present an application to wind energy research, namely the estimation of power performance curves for wind turbines.

[1] R. Friedrich et al., Physics Letters A 271 (2000), 217-222

[2] F. Böttcher et al., Physical Review Letters 97, 090603 (2006)