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Synchronization and Coarsening (without SOC) in a Forest-Fire Model

K. E. Chan·P. L. Krapivsky·S. Redner
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Abstract

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 grows linearly with time as t-->oo. The number density of patches of length L, N(L,t), scales as ^{-2}M(L/ ), and within a mean-field rate equation description we find that this scaling function decays as e^{-1/x} for x-->0, and as e^{-x} for x-->oo. 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.

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K. E. Chan, P. L. Krapivsky, S. Redner. 2002-03-18. Synchronization and Coarsening (without SOC) in a Forest-Fire Model. https://doi.org/10.1103/physreve.66.016122

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