Are Forest Fires Predictable?

Details Are Forest Fires Predictable? Are Forest Fires Predictable?

2002-04-23

arxiv.org/abs/cond-mat/0204509v1

Int. J. Mod. Phys. C13 (2002) 1017

Physics

Condensed Matter

13 pages, 13 figures

Scientific paper

10.1142/S0129183102003760

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 $p_n\to p_{n+1}$, where $p_n$ is the probability of finding a tree in a cell, and $n$ is the discrete time. We demonstrate that the time evolution of $p$ 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.

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