The study of critical phenomena that originated in the natural sciences has been extended to the financial economics' field, giving researchers new approaches to risk management, forecasting, the study of bubbles and crashes, and many kinds of problems involving complex systems with...

Unlike equilibrium systems, where it is possible to study the impact of endogenous and exogenous perturbations using fluctuation-dissipation theorems, it is difficult to understand and predict the impact of shocks in out-of-equilibrium systems. This thesis tries to uncover and quantify the...

The concept of self-organizedcriticality evolved from studies of three simplecellular-automata models: the sand-pile, slider-block,and forest-fire models. In each case, there is asteady “input” and the “loss” is associated with afractal (power-law) distribution of “avalanches.” Each...

The Barkhausen jumps or avalanches in magnetic domain-walls motion between successive pinned configurations, due the competition among magnetic external driving force and substrum quenched disorder, appear in bulk materials and thin films. We introduce a model based in rules for the domain wall...

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...