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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 networks 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.
This Letter investigates the nature of synchronization in multilayered and multiplexed populations in which the interlayer interactions are randomly pinned. First, we show that a multilayer network constructed by setting up all-to-all interlayer conn
The phenomenon of explosive synchronization, which originates from hypersensitivity to small perturbation caused by some form of frustration prevailed in various physical and biological systems, has been shown to lead events of cascading failure of t
It is known that intra-layer adaptive coupling among connected oscillators instigates explosive synchronization (ES) in multilayer networks. Taking an altogether different cue in the present work, we consider inter-layer adaptive coupling in a multip
Adaptation plays a fundamental role in shaping the structure of a complex network and improving its functional fitting. Even when increasing the level of synchronization in a biological system is considered as the main driving force for adaptation, t
Synchronization has been the subject of intense research during decades mainly focused on determining the structural and dynamical conditions driving a set of interacting units to a coherent state globally stable. However, little attention has been p