Related papers: A Bottom-Up Model of Self-Organized Criticality on…

Controlling self-organizing systems is challenging because the system responds to the controller. Here we develop a model that captures the essential self-organizing mechanisms of Bak-Tang-Wiesenfeld (BTW) sandpiles on networks, a…

The following chapter provides an overview of the techniques used to understand Self-Organised Criticality (SOC) by performing computer simulations. Those are of particular significance in SOC, given its very paradigm, the BTW…

The original sandpile model of Bak, Tang and Wiesenfeld from 1987 has inspired lots of consequent work and further ideas of how to describe the birth of scale-invariant statistics in various systems and in particular models. In this article…

With the original Bak-Tang-Wisenefeld (BTW) sandpile we uncover the $1/\varphi$ noise in the mechanism maintaining self-organized criticality (SOC) - the question raised together with the concept of SOC. We posit that the dynamics of stress…

Can the concept of self-organized criticality, exemplified by models such as the sandpile model, be described within the framework of continuous phase transitions? In this paper, we provide extensive numerical evidence supporting an…

We employ the eigen microstate approach to explore the self-organized criticality (SOC) in two celebrated sandpile models, namely, the BTW model and the Manna model. In both models, phase transitions from the absorbing-state to the critical…

We investigate, by numerical simulations, how the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model can induce emergence of scale-free (SF) networks and how this emerging structure affects dynamics of the system. We also…

Here, a scenario is proposed, according to which a generic self-organized critical (SOC) system can be looked upon as a Witten-type topological field theory (W-TFT) with spontaneously broken Becchi-Rouet-Stora-Tyutin (BRST) symmetry. One of…

We propose a one-dimensional rice-pile model which connects the 1D BTW sandpile model (Phys. Rev. A 38, 364 (1988)) and the Oslo rice-pile model (Phys. Rev. lett. 77, 107 (1997)) in a continuous manner. We found that for a sufficiently…

We introduce two sandpile models which show the same behavior of real sandpiles, that is, an almost self-organized critical behavior for small systems and the dominance of large avalanches as the system size increases. The systems become…

The concept of "self-organized criticality" (SOC) has been introduced by Bak, Tang, and Wiesenfeld (1987) to describe the statistics of avalanches on the surface of a sandpile with a critical slope, which produces a scale-free powerlaw size…

We present a unified mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF)…

``Self-Organised Criticality'' (SOC) is the mechanism by which complex systems spontaneously settle close to a *critical point*, at the edge between stability and chaos, and characterized by fat-tailed fluctuations and long-memory…

The notion of Self-organized criticality (SOC) had been conceived to interpret the spontaneous emergence of long range correlations in nature. Since then many different models had been introduced to study SOC. All of them have few common…

Avalanche dynamics is an indispensable feature of complex systems. Here we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent $\gamma$ through the Bak-Tang-Wiesenfeld (BTW) sandpile model.…

We study the BTW-height model of self-organized criticality on a square lattice with some long range connections giving to the lattice the character of small world network. We find that as function of the fraction $p$ of long ranged bonds…

We present a general conceptual framework for self-organized criticality (SOC), based on the recognition that it is nothing but the expression, ''unfolded'' in a suitable parameter space, of an underlying {\em unstable} dynamical critical…

Both the deterministic and stochastic sandpile models are studied on the percolation backbone, a random fractal, generated on a square lattice in $2$-dimensions. In spite of the underline random structure of the backbone, the deterministic…

Spatial self-similarity is a hallmark of critical phenomena. We study the dynamic process of percolation, in which bonds are incrementally added to an initially empty lattice until the system becomes fully occupied. By tracking the gap --…

We present a pedagogical introduction to self-organized criticality (SOC), unraveling its connections with nonequilibrium phase transitions. There are several paths from a conventional critical point to SOC. They begin with an…