Long-term correlations in stochastic systems with extended time-delayed feedback

The effects of a feedback with multiple time delays on noise-induced dynamics are studied in a nonlinear system close to the Hopf instability. We show analytically and numerically that such a feedback creates two distinct time scales, which can be tuned independently by the feedback parameters. In this way, the coherence of noise-induced oscillations can be drastically improved, and an arbitrarily large correlation of oscillations can be achieved without inducing a bifurcation. This opens up new perspectives for control of stochastic dynamical systems.