Improving the Frequency Precision of Oscillators by Synchronization

TL;DR

This paper investigates how synchronization of oscillators affects frequency precision, confirming N-fold improvement with dissipative coupling and showing limited improvement with reactive coupling, depending on disorder and source region dynamics.

Contribution

It provides a detailed analysis of frequency precision enhancement in synchronized oscillators, especially highlighting differences between dissipative and reactive coupling.

Findings

Frequency precision improves by a factor of N with dissipative coupling.

Reactive coupling leads to frequency precision improvement independent of N.

The improvement depends on disorder and source region dynamics in reactive coupling.

Abstract

Improving the frequency precision by synchronizing a lattice of oscillators is studied in the phase reduction limit. For the most commonly studied case of purely dissipative phase coupling (the Kuramoto model) I confirm that the frequency precision of N oscillators perturbed by independent noise sources is improved by a factor N as expected from simple averaging arguments. In the presence of reactive coupling, such as will typically be the case for non-dissipatively coupled oscillators based on high-Q resonators, the synchronized state consists of target like waves radiating from a local source which is a region of higher frequency oscillators. In this state all the oscillators evolve with the same frequency, however I show that the improvement of the frequency precision is independent of N for large N, but instead depends on the disorder and reflects the dependence of the frequency of the synchronized state on just those oscillators in the source region of the waves.