Europhys. Lett.
Volume 71, Number 3, August 2005
Page(s) 366 - 372
Section General
Published online 13 July 2005
Europhys. Lett., 71 (3), pp. 366-372 (2005)
DOI: 10.1209/epl/i2005-10100-9

Mean-field approximation of time-delayed feedback control of noise-induced oscillations in the Van der Pol system

J. Pomplun, A. Amann and E. Schöll

Institut für Theoretische Physik - Technische Universität Berlin Hardenbergstr. 36, D-10623 Berlin, Germany

received 8 April 2005; accepted in final form 7 June 2005
published online 13 July 2005

We study time-delayed feedback control of noise-induced oscillations analytically and numerically for the paradigmatic model of the Van der Pol oscillator under the influence of white noise. We focus on the regime below the Hopf bifurcation where the deterministic system has a stable fixed point and does not exhibit oscillations. Analytical expressions for the power spectral density and the coherence properties of the stochastic delay differential equation in dependence upon noise intensity, delay time, and feedback strength are derived on the basis of a mean-field approximation, and are in good agreement with our numerical simulations of the full nonlinear model. Our analytical results elucidate how the correlation time of the controlled stochastic oscillations can be maximized as a function of delay time and feedback strength.

05.40.Ca - Noise.
05.45.Gg - Control of chaos, applications of chaos.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.) .

© EDP Sciences 2005