Synchronization and frustration in oscillator networks with attractive and repulsive interactions

TL;DR

This paper investigates how mixed attractive and repulsive interactions affect synchronization stability in oscillator networks, revealing scaling laws and symmetry changes related to repulsive coupling strength.

Contribution

It provides a combined numerical and analytical analysis of synchronization stability in oscillator networks with both attractive and repulsive interactions, introducing the concept of frustration minimization.

Findings

Describes scaling properties of desynchronization transition.

Shows unsynchronized configurations have symmetry depending on repulsive interaction strength.

Uses frustration minimization to explain collective dynamics.

Abstract

We study, numerically and analytically, the stability of synchronization for an ensemble of coupled phase oscillators with attractive and repulsive interactions, as a function of the number of repulsive couplings and their intensity. Scaling properties of the desynchronization transition are disclosed, and it is shown that unsynchronized configurations have different symmetries depending on the intensity of the repulsive interaction. The concept of frustration minimization helps understanding the main features observed in the collective dynamics of the oscillator network.