Related papers: The large connectivity limit of bootstrap percolat…
Majority bootstrap percolation on the random graph $G_{n,p}$ is a process of spread of "activation" on a given realisation of the graph with a given number of initially active nodes. At each step those vertices which have more active…
We compare phase transition and critical phenomena of bond percolation on Euclidean lattices, nonamenable graphs, and complex networks. On a Euclidean lattice, percolation shows a phase transition between the nonpercolating phase and…
K-core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems. Since these models are considerably similar, it has been…
We study a one parameter family of random graph models that spans a continuum between traditional random graphs of the Erd\H{o}s-R\'enyi type, where there is no underlying structure, and percolation models, where the possible edges are…
Critical phenomena can show unusual phase diagrams when defined in complex network topologies. The case of classical phase transitions such as the classical Ising model and the percolation transition has been studied extensively in the last…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition, and…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
The percolation phase transitions of two-dimensional lattice networks under a generalized Achlioptas process (GAP) are investigated. During the GAP, two edges are chosen randomly from the lattice and the edge with minimum product of the two…
We show that the interplay between geometric criticality and dynamical fluctuations leads to a novel universality class of the contact process on a randomly diluted lattice. The nonequilibrium phase transition across the percolation…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
In majority bootstrap percolation on a graph G, an infection spreads according to the following deterministic rule: if at least half of the neighbours of a vertex v are already infected, then v is also infected, and infected vertices remain…
Bond percolation on infinite heavy-tailed power-law random networks lacks a proper phase transition; or one may say, there is a phase transition at {\em zero percolation probability}. Nevertheless, a finite size percolation threshold…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…
The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the…
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…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
By introducing a simple competition mechanism for bond insertion in random graphs, explosive percolation exhibits a sharp phase transition with rich critical phenomena. We investigate high-order connectivity in explosive percolation using…
Partially motivated by the desire to better understand the connectivity phase transition in fractal percolation, we introduce and study a class of continuum fractal percolation models in dimension d greater than or equal to 2. These include…