The emergence of weak criticality in SOC systems

¹ Centre for Complexity Science and Department of Mathematics, Imperial College London South Kensington Campus, SW7 2AZ, London, UK
² Institute of Innovative Research, Tokyo Institute of Technology - 4259, Nagatsuta-cho, Yokohama 226-8502, Japan

Received: 27 April 2018
Accepted: 25 July 2018

Abstract

Since Self-Organised Criticality (SOC) was introduced in 1987, both the nature of the self-organisation and the criticality have remained controversial. Besides, SOC-like dynamics has recently been observed in many natural processes like brain activity and rain precipitations, making a better understanding of such systems more urgent. Here we focus on the Drossel-Schwabl forest-fire model (FFM) of SOC and show that despite the model is not critical, it nevertheless exhibits a behaviour that justifies the introduction of a new kind of weak criticality. We present a method that allows to quantify the degree of criticality of a system and to introduce a new class of critical systems. This method can be easily adapted to experimental settings and contribute to a better understanding of real systems.