ARE FOREST FIRES PREDICTABLE?

K. Malarz (), S. Kaczanowska and K. Kułakowski ()
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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

International Journal of Modern Physics C (IJMPC), 2002, vol. 13, issue 08, 1017-1031

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.

Keywords: Cellular automata; chaos; percolation; symbolic dynamics (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1142/S0129183102003760

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