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| Titel |
Log-periodic behavior in a forest-fire model |
| VerfasserIn |
B. D. Malamud, G. Morein, D. L. Turcotte |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 12, no. 5 ; Nr. 12, no. 5 (2005-06-09), S.575-585 |
| Datensatznummer |
250010769
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| Publikation (Nr.) |
 copernicus.org/npg-12-575-2005.pdf |
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| Zusammenfassung |
| 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. |
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