In this paper we briefly review few self-organized critical (SOC) models of the phenomenon of earthquakes. For example, the two-dimensional non-conservative SOC model of Olami, Feder and Christensen (OFC) has been described. It is known that the effect of the fixed boundary on this model is very...

We introduce an inverse-cascade model to explain self-organized critical behavior. This model is motivated by the forest-fire model. In the forest-fire model trees are randomly planted on a grid, sparks are also dropped on the grid resulting in fires in which trees are lost. In the...

The Bak–Tang–Wiesenfeld sandpile model provides a simple and elegant system with which to demonstrate self-organized criticality. This model has rather remarkable mathematical properties first elucidated by Dhar. I demonstrate some of these properties graphically with a simple computer...

Highly correlated brain dynamics produces synchronized states with no behavioral value, while weakly correlated dynamics prevents information flow. We discuss the idea put forward by Per Bak that the working brain stays at an intermediate (critical) regime characterized by power-law correlations.

A surprisingly large number of systems in nature are thought to be governed by internal dynamics which causes avalanches of various sizes. In such systems energy, which is delivered from outside, is redistributed as a result of the occurrence of localized avalanches. Starting an avalanche...

Individual threshold behaviors generate large endogenous fluctuations in a globally interactive network. In a version of NK models, the bonds are allowed to be allocated randomly across nodes in each period. It is shown that the aggregate output asymptotically follows a branching process with...

The quenched site-diluted Ising ferromagnet, with a probability p for site occupation, is studied on a square lattice. A method, based on self-organized criticality, drives the system spontaneously to the critical point, providing an efficient way to estimate critical properties for different...

We investigate, using mean-field theory and simulation, the effect of asymmetry on the critical behavior and probability density of Bak–Sneppen models. Two kinds of anisotropy are investigated: (i) different numbers of sites to the left and right of the central (minimum) site are updated and...

Solar flares activity is investigated by looking at the statistics of the waiting times between hard X-ray bursts. It is found that the distribution has a power-law tail which indicates the existence of nontrivial dynamics with long-range correlations. A shell model for MHD turbulence is capable...

In this study we use Tsallis non-extensive statistics for a new understanding the magnetospheric dynamics and the magnetospheric self-organization during quiet and intensive superstorm periods. The qsens, qstat, and qrel indices set known as the Tsallis q-triplet was estimated during both quiet...