Forest-fire models as a bridge between different paradigms in Self-Organized Criticality

TL;DR

This paper transforms a stochastic forest-fire model into a deterministic threshold model, revealing that it shares key statistical properties with sandpile and earthquake models of Self-Organized Criticality, thus bridging different paradigms.

Contribution

It introduces a deterministic version of the forest-fire model, demonstrating its equivalence in macroscopic behavior to the original stochastic model and connecting various SOC models.

Findings

Deterministic forest-fire model reproduces the statistical properties of the stochastic version.

The model provides insights into the relation between forest-fire, sandpile, and earthquake models.

The approach bridges different paradigms within Self-Organized Criticality.

Abstract

We turn the stochastic critical forest-fire model introduced by Drossel and Schwabl (PRL 69, 1629, 1992) into a deterministic threshold model. This new model has many features in common with sandpile and earthquake models of Self-Organized Criticality. Nevertheless our deterministic forest-fire model exhibits in detail the same macroscopic statistical properties as the original Drossel and Schwabl model. We use the deterministic model and a related semi-deterministic version of the model to elaborate on the relation between forest-fire, sandpile and earthquake models.