Erdos-Renyi random graphs + forest fires = self-organized criticality

TL;DR

This paper introduces a model combining Erdos-Renyi random graphs with a lightning-induced burning process, demonstrating that the system self-organizes into a critical state under certain conditions.

Contribution

It presents a novel modification of Erdos-Renyi graphs with a burning mechanism, showing self-organized criticality in the system.

Findings

System reaches a permanent critical state under specific lightning intensities.

The model exhibits self-organized criticality behavior.

Graph connectivity dynamics are significantly affected by the burning process.

Abstract

We modify the usual Erdos-Renyi random graph evolution by letting connected clusters 'burn down' (i.e. fall apart to disconnected single sites) due to a Poisson flow of lightnings. In a range of the intensity of rate of lightnings the system sticks to a permanent critical state.