Dresden 2006 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe
DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.33: Poster
Donnerstag, 30. März 2006, 16:00–18:00, P1
Data analysis of periodically forced stochastic systems with time delay — •Andreas Wilmer, Dr. Till D. Frank, and Prof. Dr. Rudolf Friedrich — Institute for Theoretical Physics, WWU Münster, Wilhelm-Klemm-Str. 9, D-48149 Münster, Germany
A wide class of stochastic processes can be described by a system of Langevin equations.
We shall consider stochastic systems, which include periodic forces and a time delayed feedback.
These are relevant for various systems like seasonal systems in biology, engineering or movement control.
If we consider a univariate process with the stochastic variable X(t), a time delay τ and
a periodic force f(t)=f(t+T), the Langevin equation reads as follows:
| X(t) = h | ⎛ ⎝ | X(t),X(t−τ),f(t) | ⎞ ⎠ | +g | ⎛ ⎝ | X(t),X(t−τ) | ⎞ ⎠ | Γ(t) |
where Γ(t) is the fluctuating uncorrelated Langevin force with ⟨Γi(t) Γj(t′)⟩=2δijδ(t−t′),
the deterministic part D(1)=h called drift and the stochastic part g corresponding to
the diffusion coefficient D(2)=g2.
We shall present a method, which enables the discrimination of a stochastic and deterministic force of time series
and allows the estimation of the drift and diffusion coefficients from data.