Dynamic synchronization of driven self-oscillators: Modeling and experiment.

Abstract

Synchronization of self-sustained oscillators under fixed frequency and amplitude forcing is well understood, but how time-varying forcing mangles phase locking has been much less explored. Theory predicts that slow deterministic modulation of the drive amplitude or frequency can lead to a peculiar synchronization regime characterized by intermittent locking of the oscillation phase beyond the Arnold-tongue boundaries associated with fixed harmonic forcing. We test these predictions in a controllable aeroacoustic self oscillator, i.e., a whistle, that exhibits a robust limit cycle and is subject to external acoustic forcing with programmable frequency and amplitude modulation. Under both slowly varying frequency and amplitude of the forcing, three regimes are observed: (i) strict synchronization, (ii) intermittent synchronization, characterized by alternating phase-locking and brief phase-slip episodes, and (iii) no synchronization, with regular phase slips. Particularly in the strict synchronization regime, the phase of the oscillator will follow an arbitrary, slowly varying drive phase and under amplitude modulation its amplitude fluctuations are strongly suppressed.