Nonlinear Phenomena in Complex Systems, 2001, Vol.4, No.1, pp.85--89

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2001, Volume 4, Number 1, pp.85-89

Description of Undercritical and Overcritical f₀ Avalanche Hierarchy in the Bak-Sneppen Evolution Model
W. Li and X. Cai

For the Bak-Sneppen evolution model we present two master equations prescribing hierarchical structures of undercritical f₀ avalanches and overcritical ones respectively. Taylor expansions of the master equations generate two infinite series of exact equations. Solutions of the two first-leading-order equations yield two universal exponents: gamma, for "gamma" equation, and beta, for "beta" equation. It is found that gamma and beta are each determined by a scaling function, related to the configurations of the system. It is also shown that both gamma and beta equal 1 as the critical state is reached.
Key words: self-organized criticality, evolution model, master equation, undercritical avalanches, over-critical avalanches, scaling function

Full text: Acrobat PDF (137KB) PostScript (431KB) PostScript.gz (133KB)