Related papers: Sandpile cascades on interacting tree-like network…
We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional square lattice of lattice sizes up to L=4096. A detailed analysis of the probability distribution of the size, area, duration and radius of the avalanches will be…
An analysis of moments and spectra shows that, while the distribution of avalanche areas obeys finite size scaling, that of toppling numbers is universally characterized by a full, nonlinear multifractal spectrum. Rare, large avalanches…
Real-world complex systems always interact with each other, which causes these systems to collapse in an avalanche or cascading manner in the case of random failures or malicious attacks. The robustness of multilayer networks has attracted…
In a model of self-organized criticality unstable sites discharge to just one of their neighbors. For constant discharge ratio $\alpha$ and for a certain range of values of the input energy, avalanches are simple branchless P\'olya random…
We study, both analytically and numerically, the cascade of failures in two coupled network systems A and B, where multiple support-dependent relations are randomly built between nodes of networks A and B. In our model we assume that each…
In a network, a local disturbance can propagate and eventually cause a substantial part of the system to fail, in cascade events that are easy to conceptualize but extraordinarily difficult to predict. Here, we develop a statistical…
Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon…
A new model about cascading occurrences caused by perturbation is established to search after the mechanism because of which catastrophes in networks occur. We investigate the avalanche dynamics of our model on 2-dimension Euclidean…
The dynamics of cascading failures in spatial interdependent networks significantly depend on the interaction range of dependency couplings between layers. In particular, for increasing range of dependency couplings, different types of…
We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an…
As shown recently (arXiv:0801.3056), several types of neuronal complex networks involving non-linear integration-and-fire dynamics exhibit an abrupt activation along their transient regime. Interestingly, such an avalanche of activation has…
We introduce a novel tool for analyzing complex network dynamics, allowing for cascades of causally-related events, which we call causal webs (c-webs), to be separated from other non-causally-related events. This tool shows that…
In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex…
We study the two-dimensional Abelian Sandpile Model on a square lattice of linear size L. We introduce the notion of avalanche's fine structure and compare the behavior of avalanches and waves of toppling. We show that according to the…
In this paper, the Bak--Tang--Wiesenfeld model for various substrate topologies and a variety of neighborhoods is reconsidered. With computer simulation, we study the distribution of avalanche sizes. Using the Z-score we confirm that…
We live in a modern world supported by large, complex networks. Examples range from financial markets to communication and transportation systems. In many realistic situations the flow of physical quantities in the network, as characterized…
We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk…
Cascades are self-amplifying processes triggered by feedback mechanisms that may cause a substantial part of a macroscopic system to change its phase in response of a relatively small local event. The theoretical background for these…
We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the…
A sequence of bursts observed in an intermittent time series may be caused by a single avalanche, even though these bursts appear as distinct events when noise and/or instrument resolution impose a detection threshold. In the…