Related papers: Explosive Synchronization Transitions in Scale-fre…
In this Letter, we show that the explosive percolation is a novel continuous phase transition. The order-parameter-distribution histogram at the percolation threshold is studied in Erd\H{o}s-R\'{e}nyi networks, scale-free networks, and…
We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…
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…
Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…
Nowadays, explosive synchronization is a well documented phenomenon occurring in networks when the node frequency and its degree are correlated. This first-order transition, which may coexists with classical synchronization, has been…
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…
We introduce a condition for an ensemble of networked phase oscillators to feature an abrupt, first-order phase transition from an unsynchronized to a synchronized state. This condition is met in a very wide spectrum of situations, and for…
We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean field…
Explosive synchronization(ES), as one kind of abrupt dynamical transition in nonlinearly coupled systems, is currently a subject of great interests. Given a special frequency distribution, a mixed ES is observed in a ring of coupled phase…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
Heterogeneity in the degree distribution is known to suppress global synchronization in complex networks of symmetrically coupled oscillators. Scale-free networks display a great deal of heterogeneity, containing a few nodes, termed hubs,…
We study transition to phase synchronization in an ensemble of Stuart-Landau oscillators interacting on a star network. We observe that by introducing frequency weighted coupling and time scale variations in the dynamics of nodes, system…
Synchronization is an important collective phenomenon in interacting oscillatory agents. Many functional features of the brain are related to synchronization of neurons. The type of synchronization transition that may occur (explosive vs.…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
In this paper, we investigate how the internal dynamics of the systems within a network influence the transition to synchronization in adaptive networks of coupled Rossler systems. The network structure is dynamically determined by local…
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
The existence of explosive phase transitions in random (Erd\H os R\'enyi-type) networks has been recently documented by Achlioptas et al.\ [Science {\bf 323}, 1453 (2009)] via simulations. In this Letter we describe the underlying mechanism…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
We introduce the concept of synchronization bombs as large networks of coupled heterogeneous oscillators that operate in a bistable regime and abruptly transit from incoherence to phase-locking (or vice-versa) by adding (or removing) one or…
Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions have the power-law form. In this paper, we investigate the synchronization phenomena in a scale-free…