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Are Forest Fires Predictable?

Author

Listed:
  • K. MALARZ

    (Department of Theoretical and Computational Physics, Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy (AGH), al. Mickiewicza 30, PL-30059 Kraków, Poland)

  • S. KACZANOWSKA

    (Department of Theoretical and Computational Physics, Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy (AGH), al. Mickiewicza 30, PL-30059 Kraków, Poland)

  • K. KUŁAKOWSKI

    (Department of Theoretical and Computational Physics, Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy (AGH), al. Mickiewicza 30, PL-30059 Kraków, Poland)

Abstract

Dynamic mean field theory is applied to the problem of forest fires. The starting point is the Monte Carlo simulation in a lattice of a million cells. The statistics of the clusters is obtained by means of the Hoshen–Kopelman algorithm. We get the mappn→ pn + 1, wherepnis the probability of finding a tree in a cell, andnis the discrete time. We demonstrate that the time evolution ofpis chaotic. The arguments are provided by the calculation of the bifurcation diagram and the Lyapunov exponent. The bifurcation diagram reveals several windows of stability, including periodic orbits of length three, five and seven. For smaller lattices, the results of the iteration are in qualitative agreement with the statistics of the forest fires in Canada in the years 1970–2000.

Suggested Citation

  • K. Malarz & S. Kaczanowska & K. Kułakowski, 2002. "Are Forest Fires Predictable?," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1017-1031.
    • Handle: RePEc:wsi:ijmpcx:v:13:y:2002:i:08:n:s0129183102003760
    DOI: 10.1142/S0129183102003760
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    Cited by:

    1. Malarz, Krzysztof, 2023. "Random site percolation thresholds on square lattice for complex neighborhoods containing sites up to the sixth coordination zone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    2. Ali Nouh Mabdeh & A’kif Al-Fugara & Khaled Mohamed Khedher & Muhammed Mabdeh & Abdel Rahman Al-Shabeeb & Rida Al-Adamat, 2022. "Forest Fire Susceptibility Assessment and Mapping Using Support Vector Regression and Adaptive Neuro-Fuzzy Inference System-Based Evolutionary Algorithms," Sustainability, MDPI, vol. 14(15), pages 1-26, August.

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