Some fractal aspects of Self-Organized Criticality

TL;DR

This paper explores the fractal properties of Self-Organized Criticality (SOC) using dynamical systems theory, linking attractor structures to avalanche behaviors in systems exhibiting power-law distributions.

Contribution

It introduces a dynamical systems framework for SOC, employing iterated function systems and hyperbolic dynamics to analyze the structure of avalanches.

Findings

Link between attractor structure and avalanche properties

Representation of SOC dynamics via iterated function systems

Analysis of hyperbolic dynamical systems in SOC context

Abstract

The concept of Self-Organized Criticality (SOC) was proposed in an attempt to explain the widespread appearance of power-law in nature. It describes a mechanism in which a system reaches spontaneously a state where the characteristic events (avalanches) are distributed according to a power law. We present a dynamical systems approach to Self-Organized Criticality where the dynamics is described either in terms of Iterated Function Systems, or as a piecewise hyperbolic dynamical system of skew-product type. Some results linking the structure of the attractor and some characteristic properties of avalanches are discussed.