Self-organized critical forest-fire model

It is shown that the forest density in the critical state assumes its minimum possible value, i.e., that energy dissipation is maximum, and derived scaling laws and calculate all critical exponents.

Abstract

A forest-fire model is introduced which contains a lightning probability f. This leads to a self-organized critical state in the limit f\ensuremath{\rightarrow}0 provided that the time scales of tree growth and burning down of forest clusters are separated. We derive scaling laws and calculate all critical exponents. The values of the critical exponents are confirmed by computer simulations. For a two-dimensional system, we show that the forest density in the critical state assumes its minimum possible value, i.e., that energy dissipation is maximum.