Self-Organized Branching Processes: A Mean-Field Theory for Avalanches

TL;DR

This paper introduces a new mean-field model for self-organized criticality that explicitly incorporates boundary conditions, coupling local dynamics with a global control parameter to better explain avalanche phenomena.

Contribution

A novel mean-field model for self-organized criticality that accounts for boundary effects and couples local rules with a global control mechanism.

Findings

Derived avalanche size distributions analytically.

Numerical simulations confirm the model's predictions.

Highlights the importance of boundary conditions in self-organization.

Abstract

We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed mean-field theories. We introduce a new mean-field model that explicitly takes the boundary conditions into account; in this way, the local dynamical rules are coupled to a global equation that drives the control parameter to its critical value. We study the model numerically, and analytically we compute the avalanche distributions.