Explosive transitions in complex networks' structure and dynamics: percolation and synchronization

TL;DR

This paper reviews the recent discovery and understanding of explosive, first-order-like phase transitions in complex networks' structure and dynamics, focusing on percolation and synchronization phenomena.

Contribution

It provides a comprehensive review of the literature on explosive transitions in networks, highlighting key results, experimental verifications, and future research directions.

Findings

Explosive percolation causes abrupt structural changes in networks.

Explosive synchronization leads to sudden emergence of collective dynamics.

Recent studies have advanced understanding of conditions inducing explosive transitions.

Abstract

Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous and reversible. Recently, however, explosive phenomena have been reported in com- plex networks' structure and dynamics, which rather remind first-order (discontinuous and irreversible) transitions. Explosive percolation, which was discovered in 2009, corresponds to an abrupt change in the network's structure, and explosive synchronization (which is concerned, instead, with the abrupt emergence of a collective state in the networks' dynamics) was studied as early as the first models of globally coupled phase oscillators were taken into consideration. The two phenomena have stimulated investigations and de- bates, attracting attention in many relevant fields. So far, various substantial contributions and progresses (including experimental verifications) have been made, which have provided insights on what structural and dynamical properties are needed for inducing such abrupt transformations, as well as have greatly enhanced our understanding of phase transitions in networked systems. Our intention is to offer here a monographic review on the main-stream literature, with the twofold aim of summarizing the existing results and pointing out possible directions for future research.