Related papers: Continuum Theory with Memory for Avalanches in Sel…
We study a model of ``organized'' criticality, where a single avalanche propagates through an \textit{a priori} static (i.e., organized) sandpile configuration. The latter is chosen according to an i.i.d. distribution from a Borel…
Complex systems, when poised near a critical point of a phase transition between order and disorder, exhibit a dynamics comprising a scale-free mixture of order and disorder which is universal, i.e. system-independent (1-5). It allows…
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…
We investigate the conditions required for general spin systems with frustration and disorder to display self-organized criticality, a property which so far has been established only for the fully-connected infinite-range…
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…
We present generic scaling laws relating spreading critical exponents and avalanche exponents (in the sense of self-organized criticality) in general systems with absorbing states. Using these scaling laws we present a collection of the…
Avalanches, or Avalanche-like, events are often observed in the dynamical behaviour of many complex systems which span from solar flaring to the Earth's crust dynamics and from traffic flows to financial markets. Self-organized criticality…
We describe the construction of a conserved reaction-diffusion system that exhibits self-organized critical (avalanche-like) behavior under the action of a slow addition of particles. The model provides an illustration of the general…
We perform a new analysis on the dissipative Olami-Feder-Christensen model on a small world topology considering avalanche size differences. We show that when criticality appears the Probability Density Functions (PDFs) for the avalanche…
Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behaviour: These avalanches are characterized by a power law distribution for the size and…
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…
Models of self-organized criticality, which can be described as singular diffusions with or without (multiplicative) Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models), are analyzed. Existence and uniqueness of…
Plastic events in sheared glasses are considered an example of so-called avalanches, whose sizes obey a power-law probability distribution with the avalanche critical exponent $\tau$. Although mean-field theory predicts a universal value of…
The origin of self-organized criticality in a model without conservation law (Olami, Feder, and Christensen, Phys. Rev. Lett. {\bf 68}, 1244 (1992)) is studied. The homogeneous system with periodic boundary condition is found to be periodic…
The "Self-organized criticality" (SOC), introduced in 1987 by Bak, Tang and Wiesenfeld, was an attempt to explain the 1/f noise, but it rapidly evolved towards a more ambitious scope: explaining scale invariant avalanches. In two decades,…
We numerically investigate the Olami-Feder-Christensen model on a quenched random graph. Contrary to the case of annealed random neighbors, we find that the quenched model exhibits self-organized criticality deep within the nonconservative…
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…
An improved version of the Olami-Feder-Christensen model has been introduced to consider avalanche size differences. Our model well demonstrates the power-law behavior and finite size scaling of avalanche size distribution in any range of…
We derive an infinite hierarchy of exact equations for the Bak-Sneppen model in arbitrary dimensions. These equations relate different moments of temporal duration and spatial size of avalanches. We prove that the exponents of the BS model…
In recent years self organised critical neuronal models have provided insights regarding the origin of the experimentally observed avalanching behaviour of neuronal systems. It has been shown that dynamical synapses, as a form of short-term…