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Tipping elements in the Earth System receive increased scientific attention over the recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element…
A phase diagram for a one-dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding the dynamics of the model: strength of disorder and range of stress relaxation. When the range of stress…
We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for…
Our recent study on the Bethe lattice reported that a discontinuous percolation transition emerges as the number of occupied links increases and each node rewires its links to locally suppress the growth of neighboring clusters. However,…
We investigate robustness of correlated networks against propagating attacks modeled by a susceptible-infected-removed model. By Monte-Carlo simulations, we numerically determine the first critical infection rate, above which a global…
A coupled phase-oscillator model consists of phase-oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is…
We propose the $K$-selective percolation process as a model for the iterative removals of nodes with the specific intermediate degree in complex networks. In the model, a random node with degree $K$ is deactivated one by one until no more…
In two dimensions, the average electrical conductance from a point in a percolating network to the network boundary should be related by a conformal transformation to the conductance from one point to another in an unbounded network. We…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
Complex networks display various types of percolation transitions. We show that the degree distribution and the degree-degree correlation alone are not sufficient to describe diverse percolation critical phenomena. This suggests that a…
Our current world is linked by a complex mesh of networks where information, people and goods flow. These networks are interdependent each other, and present structural and dynamical features different from those observed in isolated…
We propose a bond-percolation model intended to describe the consumption, and eventual exhaustion, of resources in transport networks. Edges forming minimum-length paths connecting demanded origin-destination nodes are removed if below a…
The emergence and evolution of real-world systems have been extensively studied in the last few years. However, equally important phenomena are related to the dynamics of systems' collapse, which has been less explored, especially when they…
We study the geometrical features of the order parameter's fluctuations near the critical point of mixed-order phase transitions in randomly interdependent spatial networks. In contrast to continuous transitions, where the structure of the…
In complex networks, the failure of one or very few nodes may cause cascading failures. When this dynamical process stops in steady state, the size of the giant component formed by remaining un-failed nodes can be used to measure the…
We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…
We study the behavior of scale-free networks, having connectivity distribution P(k) k^-a, close to the percolation threshold. We show that for networks with 3<a<4, known to undergo a transition at a finite threshold of dilution, the…
Self-organization of robust and efficient networks is important for a future design of communication or transportation systems, because both characteristics are not coexisting in many real networks. As one of the candidates for the…
The increased complexity of infrastructure systems has resulted in critical interdependencies between multiple networks---communication systems require electricity, while the normal functioning of the power grid relies on communication…
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…