Suppression of Noise-Induced Modulations in Multidelay Systems

Many physical systems involve time-delayed feedback or coupling. In such delay systems, noise can give rise to undesirable oscillations at frequencies resonant to the delay times. We investigate how an additional feedback term can suppress noise-induced modulations in delay systems with self-feedback that exhibit deterministic oscillatory dynamics. A simple characteristic equation is derived to predict optimal delay times for the prototypical example of a Stuart-Landau oscillator subject to two feedback terms. We then show that a characteristic equation of the same form accurately describes the dominant Floquet modes of more complex oscillatory systems and hence can be used to optimize the suppression of noise-induced modulations. This is shown for mode-locked lasers and FitzHugh-Nagumo oscillators subject to self-feedback.