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Length scales and power laws in the two-dimensional forest-fire model

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  • Honecker, A.
  • Peschel, I.

Abstract

We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two-point correlation function of trees. We check resp. improve previously obtained values for other critical exponents and perform a first investigation of the critical behaviour of the slowest relaxational mode. We also investigate the possibility of describing the critical point in terms of a distribution of the global density. We find that some qualitative features such as a temporal oscillation and a power law of the cluster-size distribution can nicely be obtained from such a model that discards the spatial structure.

Suggested Citation

  • Honecker, A. & Peschel, I., 1997. "Length scales and power laws in the two-dimensional forest-fire model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 239(4), pages 509-530.
    • Handle: RePEc:eee:phsmap:v:239:y:1997:i:4:p:509-530
    DOI: 10.1016/S0378-4371(97)00002-2
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    1. Drossel, B. & Schwabl, F., 1992. "Self-organized criticality in a forest-fire model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 47-50.
    2. Honecker, A. & Peschel, I., 1996. "Critical properties of the one-dimensional forest-fire model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 229(3), pages 478-500.
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    Cited by:

    1. Ghermandi, Luciana & Lasaponara, Rosa & Telesca, Luciano, 2010. "Intra-annual time dynamical patterns of fire sequences observed in Patagonia (Argentina)," Ecological Modelling, Elsevier, vol. 221(1), pages 94-97.

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