Explosive transitions to synchronization in networked phase oscillators

TL;DR

This paper identifies a universal condition for abrupt, first-order synchronization transitions in networked phase oscillators, highlighting the role of frequency-degree correlations and offering insights for engineering such states in practical systems.

Contribution

It introduces a broad condition for explosive synchronization in networked oscillators and explores how to relax and extend this condition for real-world applications.

Findings

Abrupt synchronization transitions are linked to frequency-degree correlations.

The condition applies across various oscillator types and initial distributions.

Methods to engineer magnetic-like synchronized states are discussed.

Abstract

We introduce a condition for an ensemble of networked phase oscillators to feature an abrupt, first-order phase transition from an unsynchronized to a synchronized state. This condition is met in a very wide spectrum of situations, and for various oscillators' initial frequency distributions. We show that the occurrence of such transitions is always accompanied by the spontaneous emergence of frequency-degree correlations in random network architectures. We also discuss ways to relax the condition, and to further extend the possibility for the first-order transition to occur, and illustrate how to engineer magnetic-like states of synchronization. Our findings thus indicate how to search for abrupt transitions in real-world applications.