Dynamic Synchronization of Driven Self-Oscillators: Modeling and Experiment

TL;DR

This study explores how slow, time-varying external forcing affects phase locking in self-oscillators, revealing regimes of strict, intermittent, and no synchronization through experiments with a controllable aeroacoustic whistle.

Contribution

It provides experimental validation of theoretical predictions on the effects of slow amplitude and frequency modulation on oscillator synchronization regimes.

Findings

Identification of three synchronization regimes: strict, intermittent, and none.

Demonstration that phase can follow arbitrary slow drive phase in strict synchronization.

Amplitude fluctuations are suppressed under amplitude modulation in the strict synchronization regime.

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 or 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 strict synchronization regime, the phase of the oscillator will follow arbitrary slowly-varying drive phase and under amplitude modulation its amplitude fluctuations are strongly suppressed.