Explosive synchronization in weighted complex networks

TL;DR

This paper introduces a practical weighting method for complex networks of oscillators that induces and enhances explosive synchronization transitions, with controllable hysteresis, supported by extensive numerical and analytical evidence.

Contribution

It proposes a novel weighting procedure based on local and global network information to induce explosive synchronization in complex networks.

Findings

The weighting method effectively induces explosive synchronization.

The procedure is scalable across different network types and frequency distributions.

Hysteresis width and extent can be parametrically controlled.

Abstract

The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic frequency distribution, we show how combining dynamical local information on frequency mismatches and global information on the graph topology suggests a judicious and yet practical weighting procedure which is able to induce and enhance explosive, irreversible, transitions to synchronization. We report extensive numerical and analytical evidence of the validity and scalability of such a procedure for different initial frequency distributions, for both homogeneous and heterogeneous networks, as well as for both linear and non linear weighting functions. We furthermore report on the possibility of parametrically controlling the width and extent of the hysteretic region of coexistence of the unsynchronized and synchronized states.