A perturbative approach to the Bak-Sneppen Model

Details A perturbative approach to the Bak-Sneppen Model A perturbative approach to the Bak-Sneppen Model

2001-01-04

arxiv.org/abs/cond-mat/0101039v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures, to be published on Physical Review Letters

Scientific paper

10.1103/PhysRevLett.86.1896

We study the Bak-Sneppen model in the probabilistic framework of the Run Time Statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing Self-Organized Criticality. The dynamics is characterized by a self-organization of almost all the species fitnesses above a non-trivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in {\em avalanches} of activity power law distributed. In this letter we use the RTS approach to compute the value of $x_c$, the value of the avalanche exponent $\tau$ and the asymptotic distribution of minimal fitnesses.

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