Control of noise-induced oscillations by delayed feedback

We propose a method to control noise-induced motion, based on using delayed feedback in the form of the difference between the delayed and the current states of the system. The method is applied to two different types of systems, namely, a self-oscillator near Andronov–Hopf bifurcation and a threshold system. In both cases, we demonstrate that by variation of time delay one can effectively control coherence and timescales of stochastic oscillations. The entrainment of the basic period of oscillations by time delay is discovered. We give explanations of the phenomena observed and provide a theory for the system near bifurcation.