Affiliation:
1. 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 map pn → pn + 1, where pn is the probability of finding a tree in a cell, and n is the discrete time. We demonstrate that the time evolution of p is 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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Computational Theory and Mathematics,Computer Science Applications,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
14 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献