Perfect synchronization in networks of phase-frustrated oscillators

TL;DR

This paper presents a method to achieve perfect synchronization in networks of phase-frustrated oscillators by strategically selecting optimal natural frequencies, applicable to various real-world systems like power grids.

Contribution

It introduces a constructive approach to determine the optimal frequency set for synchronization in phase-frustrated networks, a problem previously considered challenging.

Findings

High synchronization levels near the optimal frequency set

Method effective on both model and real power grid networks

Allows some frequency deviation without losing synchronization

Abstract

Synchronizing phase frustrated Kuramoto oscillators, a challenge that has found applications from neuronal networks to the power grid, is an eluding problem, as even small phase-lags cause the oscillators to avoid synchronization. Here we show, constructively, how to strategically select the optimal frequency set, capturing the natural frequencies of all oscillators, for a given network and phase-lags, that will ensure perfect synchronization. We find that high levels of synchronization are sustained in the vicinity of the optimal set, allowing for some level of deviation in the frequencies without significant degradation of synchronization. Demonstrating our results on first and second order phase-frustrated Kuramoto dynamics, we implement them on both model and real power grid networks, showing how to achieve synchronization in a phase frustrated environment.