An inverse-cascade model for self-organized critical behavior

We introduce an inverse-cascade model to explain self-organized critical be havior. This model is motivated by the forest-fire model. In the forest-fir e model trees are randomly planted on a grid, sparks are also dropped on th e grid resulting in fires in which trees are lost. In the inverse-cascade m odel single trees are introduced and these combine to form larger and large r clusters. This is the inverse cascade and gives a power-law (fractal) fre quency-size distribution of clusters. Model fires eliminate trees from all cluster sizes but significant numbers of trees are lost only from the large st clusters and this loss terminates the power-law scaling. Finally, our mo del illustrates important differences between critical and self-organized c ritical behavior. (C) 1999 Elsevier Science B.V. All rights reserved.