Related papers: Self-organized model of cascade spreading
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of…
This paper describes a model for power distribution network, which is hten utilized for eigenvalue behavior distribution analysis. We utilized the compensation theory to model the event that occurs in the network and derived the relation…
Understanding how contagions (information, infections, etc) are spread on complex networks is important both from practical as well as theoretical point of view. Considerable work has been done in this regard in the past decade or so.…
We propose a branching process based on a dynamical scaling hypothesis relating time and mass. In the context of earthquake occurrence, we show that experimental power laws in size and time distribution naturally originate solely from this…
Cascading failure models are typically used to capture the phenomenon where failures possibly trigger further failures in succession, causing knock-on effects. In many networks this ultimately leads to a disintegrated network where the…
We explore in the mean-field approximation the robustness with respect to dissipation of self-organized criticality in sandpile models. To this end, we generalize a recently introduced self-organized branching process, and show that the…
We investigate hierarchical structure in various complex systems according to Minimum Spanning Tree methods. Firstly, we investigate stock markets where the graphis obtained from the matrix of correlations coefficient computed between all…
Many natural phenomena exhibit power law behaviour in the distribution of event size. This scaling is successfully reproduced by Self Organized Criticality (SOC). On the other hand, temporal occurrence in SOC models has a Poisson-like…
Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…
The size distribution of planned and forced outages and following restoration times in power systems have been studied for almost two decades and has drawn great interest as they display heavy tails. Understanding of this phenomenon has…
Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here we attempt to describe it using an AC threshold…
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk…
We study slowly pulling block-spring models in random media. Second-order phase transitions exist in a model pulled by a constant force in the case of velocity-strengthening friction. If external forces are slowly increased, nearly critical…
This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes and degree distributions, identifying four regimes: (i) a dense…
We analyze a two-dimensional spring network model comprising breakable and unbreakable springs. Computer simulations showed this system to exhibit intermittent stress drops in a larger strain regime, and these stress drops resulted in…
Carreras, Dobson and colleagues have studied empirical data on the sizes of the blackouts in real grids and modeled them by computer simulations using the direct current approximation. They have found that the resulting blackout sizes are…
In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…