Are Forest Fires Predictable?
K. Malarz, S. Kaczanowska, K. Kulakowski

TL;DR
This paper applies dynamic mean field theory and Monte Carlo simulations to analyze forest fire predictability, revealing chaotic behavior and stability windows in the evolution of forest density.
Contribution
It introduces a novel application of mean field theory and bifurcation analysis to forest fire modeling, linking microscopic simulations with macroscopic dynamics.
Findings
Time evolution of forest density is chaotic.
Bifurcation diagram shows stability windows and periodic orbits.
Results qualitatively match historical forest fire data.
Abstract
Dynamic mean field theory is applied to the problem of forest fires. The starting point is the Monte Carlo simulation in a lattice of million cells. The statistics of the clusters is obtained by means of the Hoshen--Kopelman algorithm. We get the map , where is the probability of finding a tree in a cell, and is the discrete time. We demonstrate that the time evolution of is chaotic. The arguments are provided by the calculation of the bifurcation diagram and the Lyapunov exponent. The bifurcation diagram reveals several windows of stability, including periodic orbits of length three, five and seven. For smaller lattices, the results of the iteration are in qualitative agreement with the statistics of the forest fires in Canada in years 1970--2000.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
