mathematics stochastic delay-differential equations noise-induced oscillations control
We study the effect of a time-delayed feedback upon a Van der Pol oscillator under the influence
of white noise in the regime below the Hopf bifurcation where the deterministic system has a stable
fixed point. We show that both the coherence and the frequency of the noise-induced oscillations
can be controlled by varying the delay time and the strength of the control force. Approximate
analytical expressions for the power spectral density and the coherence properties of the stochastic
delay differential equation are developed, and are in good agreement with our numerical simulations.
Our analytical results elucidate how the correlation time of the controlled stochastic oscillations can
be maximized as a function of delay and feedback strength.