Experimental Study of Synchronization of Coupled Electrical Self-Oscillators and Comparison to the Sakaguchi-Kuramoto model

TL;DR

This study experimentally investigates the synchronization behavior of coupled Wien-bridge oscillators, demonstrating that their phase dynamics align with the Sakaguchi-Kuramoto model and analyzing the formation of synchronized clusters.

Contribution

It provides a detailed experimental validation of the Sakaguchi-Kuramoto model using Wien-bridge oscillators and explores cluster formation in a coupled oscillator ensemble.

Findings

Coupling behavior matches Sakaguchi-Kuramoto model predictions.

Synchronized clusters form depending on coupling strength.

Initial cluster formation influences unsynchronized oscillators.

Abstract

We explore the collective phase dynamics of Wien-bridge oscillators coupled resistively. We carefully analyze the behavior of two coupled oscillators, obtaining a transformation from voltage to effective phase. From the phase dynamics we show that the coupling can be quantitatively described by Sakaguchi's modification to the Kuramoto model. We also examine an ensemble of oscillators whose frequencies are taken from a flat distribution within a fixed frequency interval. We characterize in detail the synchronized cluster, its initial formation, as well as its effect on unsynchronized oscillators, all as a function of a global coupling strength.