The Emergence of Weak Criticality in SOC systems

TL;DR

This paper investigates the forest-fire model within SOC systems, revealing a form of weak criticality that explains behaviors observed in real systems like rain and brain activity, despite the model not being fully critical.

Contribution

It introduces the concept of weak criticality in SOC systems, providing a new perspective on their dynamics and relevance to real-world phenomena.

Findings

The forest-fire model exhibits weak criticality despite not being fully critical.

Real systems like rain and brain activity show dynamics similar to weak criticality.

Weak criticality offers a new framework to understand SOC-like behaviors.

Abstract

Since Self-Organised Criticality (SOC) was introduced in 1987, both the nature of the self-organisation and the criticality remains controversial. Recent observations on rain precipitation and brain activity suggest that real systems display a dynamics that is similar to the one observed in SOC systems, making a better understanding of such systems more urgent. Here we focus on the Drossel-Schwable forest-fire model (FFM) of SOC and show that despite the model has been proved to not being critical, it nevertheless exhibits a behavior that justifies the introduction of a new kind of $\textit{weak}$ criticality.