Forest fires and other examples of self-organized criticality

Abstract

We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of the initial conditions and without fine tuning of the parameters. After an introduction, we define the rules of the model and discuss various large-scale structures which may appear in this system. The origin of the critical behaviour is explained, critical exponents are introduced and scaling relations between the exponents are derived. Results of computer simulations and analytical calculations are summarized. The existence of an upper critical dimension and the universality of the critical behaviour under changes of lattice symmetry or the introduction of immunity are discussed. A survey of interesting modifications of the forest-fire model is given. Finally, several other important SOC models are briefly described.