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Forest-fire model with immune trees

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  • Drossel, B.
  • Schwabl, F.

Abstract

We present a generalization of the forest-fire model of P. Bak et al. by including the immunity g which is the probability that a tree is not ignited although one of its neighbors is burning. When g reaches a critical value gc(p), which depends on the tree growth rate p, the fire cannot survive any more, i.e. a continuous phase transition takes place from a steady state with fire to a steady state without fire. We present results of computer simulations and explain them by analytic calculations. The fire spreading at the phase transition represents a new type of percolation which is called “fluctuating site percolation”.

Suggested Citation

  • Drossel, B. & Schwabl, F., 1993. "Forest-fire model with immune trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 199(2), pages 183-197.
    • Handle: RePEc:eee:phsmap:v:199:y:1993:i:2:p:183-197
    DOI: 10.1016/0378-4371(93)90001-K
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    References listed on IDEAS

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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.
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    1. Alexander Veremyev & Konstantin Pavlikov & Eduardo L. Pasiliao & My T. Thai & Vladimir Boginski, 2019. "Critical nodes in interdependent networks with deterministic and probabilistic cascading failures," Journal of Global Optimization, Springer, vol. 74(4), pages 803-838, August.
    2. Lara-Sagahón, A. & Govezensky, T. & Méndez-Sánchez, R.A. & José, M.V., 2006. "A lattice-based model of rotavirus epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 525-537.
    3. Bruce Malamud & Donald Turcotte, 1999. "Self-Organized Criticality Applied to Natural Hazards," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 20(2), pages 93-116, November.
    4. Albano, Ezequiel V., 1995. "Spreading analysis and finite-size scaling study of the critical behavior of a forest fire model with immune trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 216(3), pages 213-226.
    5. Alexander Shiroky & Andrey Kalashnikov, 2021. "Mathematical Problems of Managing the Risks of Complex Systems under Targeted Attacks with Known Structures," Mathematics, MDPI, vol. 9(19), pages 1-11, October.
    6. Lin, Jianyi & Rinaldi, Sergio, 2009. "A derivation of the statistical characteristics of forest fires," Ecological Modelling, Elsevier, vol. 220(7), pages 898-903.

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