Generic criterion for explosive synchronization in heterogeneous phase oscillator populations

TL;DR

This paper establishes an exact criterion for explosive synchronization in coupled phase oscillator populations, linking dynamical and structural disorder, advancing understanding of abrupt phase transitions in complex systems.

Contribution

It provides a precise, analytical condition for explosive synchronization, moving beyond previous ad-hoc approaches in the study of complex oscillator networks.

Findings

Derives an exact criterion for explosive synchronization

Links dynamical and structural disorder in oscillator ensembles

Facilitates understanding of abrupt phase transitions

Abstract

Ordered and disordered behavior in large ensembles of coupled oscillators map to different functional states in a wide range of applications, e.g., active and resting states in the brain and stable and unstable power grid configurations. For this reason, explosive synchronization transitions, which facilitate fast, abrupt changes between these functional states, has recently seen significant interest from researchers. While previous work has identified properties of complex systems that support explosive synchronization, these investigations have been conducted largely on an ad-hoc basis. Here we provide an exact criterion for explosive synchronization in coupled phase oscillator ensembles by investigating the necessary relationship between dynamical and structural disorder. This result provides a critical step towards untangling the intertwined properties of complex systems responsible for abrupt phase transitions and bistability in biological and engineered systems.