Investigation of the forest-fire model on a small-world network.

It is shown that the forest-fire model of Bak et al. run on a square lattice network with additional long-range interactions in the spirit of a small-world network results in a scale-free system reminiscent of self-organized criticality without recourse to fine tuning. As the number of these long-range interactions is increased, the cluster size distribution exponent is found to decrease in magnitude as the small-world regime is entered, indicating a change in its universality class. It is suggested that such a model could have applicability in the study of disease spreading in human populations.

[1]  M. Newman,et al.  Scaling and percolation in the small-world network model. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Holger Kantz,et al.  On a forest fire model with supposed self-organized criticality , 1991 .

[3]  Drossel,et al.  Self-organized critical forest-fire model. , 1992, Physical review letters.

[4]  B. Hayes.  Graph Theory in Practice: Part II , 2000, American Scientist.

[5]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[6]  P. Bak,et al.  A forest-fire model and some thoughts on turbulence , 1990 .

[7]  Sheng-You Huang,et al.  Network-induced nonequilibrium phase transition in the "game of Life". , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Christensen,et al.  Self-organized critical forest-fire model: Mean-field theory and simulation results in 1 to 6 dimenisons. , 1993, Physical review letters.

[9]  Drossel,et al.  Scaling laws and simulation results for the self-organized critical forest-fire model. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.