The Emergence of Weak Criticality in SOC systems

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.