The Self-Organized Critical Forest-Fire Model with Trees and Bushes

1995 ◽  
Vol 5 (9) ◽  
pp. 1233-1238 ◽  
Author(s):  
B. Strocka ◽  
J. A.M.S. Duarte ◽  
M. Schreckenberg
Keyword(s):  
Forest Fire ◽  
The Self ◽  
Fire Model ◽  
Self Organized ◽  
Forest Fire Model

scholarly journals Universality in the One-Dimensional Self-Organized Critical Forest-Fire Model

1994 ◽  
Vol 49 (9) ◽  
pp. 856-860
Author(s):  
Barbara Drossel ◽  
Siegfried Clar ◽  
Franz Schwabl
Keyword(s):  
Size Distribution ◽  
Forest Fire ◽  
Nearest Neighbor ◽  
The Self ◽  
One Dimension ◽  
Fire Model ◽  
One Dimensional ◽  
Self Organized ◽  
Forest Fire Model ◽  
The One

Abstract We modify the rules of the self-organized critical forest-fire model in one dimension by allowing the fire to jum p over holes of ≤ k sites. An analytic calculation shows that not only the size distribution of forest clusters but also the size distribution of fires is characterized by the same critical exponent as in the nearest-neighbor model, i.e. the critical behavior of the model is universal. Computer simulations confirm the analytic results.

scholarly journals Finite-size effects in the self-organized critical forest-fire model

2000 ◽  
Vol 15 (1) ◽  
pp. 177-185 ◽  
Author(s):  
K. Schenk ◽  
B. Drossel ◽  
S. Clar ◽  
F. Schwabl
Keyword(s):  
Forest Fire ◽  
Size Effects ◽  
Finite Size ◽  
The Self ◽  
Finite Size Effects ◽  
Fire Model ◽  
Self Organized ◽  
Forest Fire Model

Forest Fires

2017 ◽  
Author(s):  
Paul Charbonneau
Keyword(s):  
Forest Fire ◽  
Forest Fires ◽  
Model Simulation ◽  
Percolation Cluster ◽  
Natural Process ◽  
Wildfire Management ◽  
Fire Model ◽  
Self Organized ◽  
Forest Fire Model ◽  
Self Organized Criticality

This chapter explores how a “natural” process generates dynamically something that is conceptually similar to a percolation cluster by using the case of forest fires. It first provides an overview of the forest-fire model, which is essentially a probabilistic cellular automata, before discussing its numerical implementation using the Python code. It then describes a representative simulation showing the triggering, growth, and decay of a large fire in a representative forest-fire model simulation on a small 100 x 100 lattice. It also considers the behavior of the forest-fire model as well as its self-organized criticality and concludes with an analysis of the advantages and limitations of wildfire management. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.

scholarly journals Exact results for the one-dimensional self-organized critical forest-fire model

1993 ◽  
Vol 71 (23) ◽  
pp. 3739-3742 ◽  
Author(s):  
Barbara Drossel ◽  
Siegfried Clar ◽  
Franz Schwabl
Keyword(s):  
Forest Fire ◽  
Exact Results ◽  
Fire Model ◽  
One Dimensional ◽  
Self Organized ◽  
Forest Fire Model ◽  
The One

SELF ORGANIZATION IN A FOREST-FIRE MODEL

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 1022-1029 ◽  
Author(s):  
B. DROSSEL ◽  
F. SCHWABL
Keyword(s):  
Forest Fire ◽  
Critical Line ◽  
Continuous Phase ◽  
Excitable Media ◽  
Fire Model ◽  
Fire Propagation ◽  
Self Organized ◽  
Forest Fire Model ◽  
New Type ◽  
Fire Spreading

We generalize the forest-fire model of P. Bak et al., which contains a tree nearest growth probability p and fire spreading to the neighbors, by including a lightning probability f and an immunity g which is the probability that a tree catches no fire although one of its neighbors is burning. The model becomes self-organized critical in the limit f/p→0, provided the time scales of tree growth and burning down of forest clusters are separated. The size distribution of forest clusters obeys a power law. We calculate the critical exponents in one dimension. A continuous phase transition is observed in the general forest-fire model when g reaches its critical value. We determine the critical line gC(p) and show that the critical fire propagation represents a new type of percolation. Finally, we point out similarities between the forest-fire model and excitable media, which comprise such different systems as chemical reactions, spreading of diseases and populations, and propagation of electrical activity in neurons.

Fractality and Self-Organized Criticality of Wars

Fractals ◽  
1998 ◽  
Vol 06 (04) ◽  
pp. 351-357 ◽  
Author(s):  
D. C. Roberts ◽  
D. L. Turcotte
Keyword(s):  
Forest Fire ◽  
Power Law ◽  
Forest Fires ◽  
Size Dependence ◽  
Fire Model ◽  
Self Organized ◽  
Battle Deaths ◽  
Forest Fire Model ◽  
Alternative Measures ◽  
Self Organized Criticality

This paper considers the frequency-size statistics of wars. Using several alternative measures of the intensity of a war in terms of battle deaths, we find a fractal (power-law) dependence of number on intensity. We show that the frequency-size dependence of forest fires is essentially identical to that of wars. The forest-fire model provides a basis for understanding the distribution of forest firest in terms of self-organized criticality. We extend the analogy to wars in terms of the initial ignition (outbreak of war) and its spread to a group of metastable countries.

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