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 …

The emergence of large-scale connectivity and synchronization are crucial to the structure,
function and failure of many complex socio-technical networks. Thus, there is great interest …

The emergence of large-scale connectivity on an underlying network or lattice, the so-called
percolation transition, has a profound impact on the system's macroscopic behaviours …

We study four Achlioptas-type processes with “explosive” percolation transitions. All
transitions are clearly continuous, but their finite size scaling functions are not entirely …

During the past two decades, percolation has long served as a basic paradigm for network
resilience, community formation and so on in complex systems. While the percolation …

By introducing a simple competition mechanism for bond insertion in random graphs,
explosive percolation exhibits a sharp phase transition with rich critical phenomena. We …

Discontinuous percolation transitions and the associated tricritical points are manifest in a
wide range of both equilibrium and nonequilibrium cooperative phenomena. To …

We develop a percolation model motivated by recent experimental studies of gels with active
network remodeling by molecular motors. This remodeling was found to lead to a critical …

The BFW model introduced by Bohman, Frieze, and Wormald [Random Struct. Algorithms,
25, 432 (2004) 1042-9832 10.1002/rsa. 20038], and recently investigated in the framework …

We consider a class of percolation models, called Achlioptas processes, discussed in
Science 323, 1453 (2009) SCIEAS 0036-8075 10.1126/science. 1167782 and Science 333 …