Related papers: Self-Organized Branching Processes: A Mean-Field T…
The well known Sandpile model of self-organized criticality generates avalanches of all length and time scales, without tuning any parameters. In the original models the external drive is randomly selected. Here we investigate a drive which…
Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For…
Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (non-conservative) local dynamics on the…
Based on a theoretical model for opinion spreading on a network, through avalanches, the effect of external field is now considered, by using methods from non-equilibrium statistical mechanics. The original part contains the implementation…
We explore the connection between self-organized criticality and phase transitions in models with absorbing states. Sandpile models are found to exhibit criticality only when a pair of relevant parameters - dissipation epsilon and driving…
Self-organized criticality can be translated into the language of absorbing state phase transitions. Most models for which this analogy is established have been investigated for their absorbing state characteristics. In this article, we…
We investigate a random--neighbours version of the two dimensional non-conserving earthquake model of Olami, Feder and Christensen [Phys. Rev. Lett. {\bf 68}, 1244 (1992)]. We show both analytically and numerically that criticality can be…
A new quantity, average fitness, is introduced in Bak-Sneppen evolution model. Through this new quantity, a new hierarchy of avalanches is observed in the evolution of Bak-Sneppen model. An exact gap equation, governing the…
The self-organized critical state is characterized by a power law distribution of cluster sizes and other properties. However experiments with sand and rice piles reveal distributions of avalanche sizes which are not power law distributed.…
Avalanches of grain displacements can be generated by creating local voids within the interior of a granular material at rest in a bin. Modeling such a two-dimensional granular system by a collection of mono-disperse discs, the system on…
In this paper we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate how they should perform in a…
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…
A minimal model for self-organized critical percolation on directed graphs with activating and de-activating links is studied. Unlike classical self-organized criticality, the variables that determine criticality are separated from the…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
The observation of apparent power-laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a…
Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for…
We derive a general formulation of the self-organized branching process by considering sandpile dynamics in an evolving population characterized by "birth" (excitation) and "death" (de-excitation) of active sites ($z=1$). New active sites…
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…
We investigate the breakdown of disordered networks under the action of an increasing external---mechanical or electrical---force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By…
A multi-type branching process is introduced to mimic the evolution of the avalanche activity and determine the critical density of the Abelian Manna model. This branching process incorporates partially the spatio-temporal correlations of…