| Volumes and Issues Contents of Issue 5 |
www.nonlin-processes-geophys.net/12/575/2005/
© Author(s) 2005. This work is licensed
under a Creative Commons License.
Log-periodic behavior in a forest-fire model
1Environmental Monitoring and Modelling Research Group, Department of Geography, King’s College London, Strand, London, WC2R 2LS, UK
2Center for Computational Science and Engineering, University of California, Davis, CA 95616, USA
3Department of Geology, University of California, Davis, CA 95616, USA
Abstract. This paper explores log-periodicity in a forest-fire cellular-automata model. At each time step of this model a tree is dropped on a randomly chosen site; if the site is unoccupied, the tree is planted. Then, for a given sparking frequency, matches are dropped on a randomly chosen site; if the site is occupied by a tree, the tree ignites and an "instantaneous" model fire consumes that tree and all adjacent trees. The resultant frequency-area distribution for the small and medium model fires is a power-law. However, if we consider very small sparking frequencies, the large model fires that span the square grid are dominant, and we find that the peaks in the frequency-area distribution of these large fires satisfy log-periodic scaling to a good approximation. This behavior can be examined using a simple mean-field model, where in time, the density of trees on the grid exponentially approaches unity. This exponential behavior coupled with a periodic or near-periodic sparking frequency also generates a sequence of peaks in the frequency-area distribution of large fires that satisfy log-periodic scaling. We conclude that the forest-fire model might provide a relatively simple explanation for the log-periodic behavior often seen in nature.
Full Article (PDF, 2673 KB)
Citation: Malamud, B. D., Morein, G., and Turcotte, D. L.: Log-periodic behavior in a forest-fire model, Nonlin. Processes Geophys., 12, 575-585, 2005. Bibtex EndNote Reference Manager
