Forest fires and other examples of self-organized criticality

Abstract

We review the properties of the self-organized critical (SOC) forest-fire\nmodel. The paradigm of self-organized criticality refers to the tendency of\ncertain large dissipative systems to drive themselves into a critical state\nindependent of the initial conditions and without fine-tuning of the\nparameters. After an introduction, we define the rules of the model and discuss\nvarious large-scale structures which may appear in this system. The origin of\nthe critical behavior is explained, critical exponents are introduced, and\nscaling relations between the exponents are derived. Results of computer\nsimulations and analytical calculations are summarized. The existence of an\nupper critical dimension and the universality of the critical behavior under\nchanges of lattice symmetry or the introduction of immunity are discussed. A\nsurvey of interesting modifications of the forest-fire model is given. Finally,\nseveral other important SOC models are briefly described.\n