Synchronization and coarsening (without self-organized criticality) in a forest-fire model.
We study the long-time dynamics of a forest-fire model with deterministic tree growth and instantaneous burning of entire forests by stochastic lightning strikes. Asymptotically the system organizes into a coarsening self-similar mosaic of synchronized patches within which trees regrow and burn simultaneously. We show that the average patch length <L> grows linearly with time as t--> infinity. The number density of patches of length L, N(L,t), scales as <L>-2N(L/<L>), and within a mean-field rate equation description we find that this scaling function decays as N(x) approximately e(-1/x) for x-->0, and as e(-x) for x--> infinity. In one dimension, we develop an event-driven cluster algorithm to study the asymptotic behavior of large systems. Our numerical results are consistent with mean-field predictions for patch coarsening.
Chan
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Center for BioDynamics, Center for Polymer Studies, and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Krapivsky
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Redner
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