Critical exponents of the anisotropic Bak-Sneppen model

Abstract

We analyze the behavior of spatially anisotropic Bak-Sneppen model. We demonstrate that a nontrivial relation between critical exponents tau and mu=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its anisotropic version as well. For one-dimensional anisotropic Bak-Sneppen model we derive a novel exact equation for the distribution of avalanche spatial sizes, and extract the value gamma=2 for one of the critical exponents of the model. Other critical exponents are then determined from previously known exponent relations. Our results are in excellent agreement with Monte Carlo simulations of the model as well as with direct numerical integration of the new equation.

8 pages, three figures included with psfig, some rewriting, + extra figure and table of exponents

References in corpus (3)

• On the High-dimensional Bak-Sneppen model
• Expansion Around the Mean-Field Solution of the Bak-Sneppen Model
• The Anisotropic Bak-Sneppen Model

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• On the thresholds, probability densities, and critical exponents of Bak-Sneppen-like models
• On singular probability densities generated by extremal dynamics
• Branching Process in a Stochastic Extremal Model
• Damage spreading in 2-dimensional isotropic and anisotropic Bak-Sneppen models
• Asymmetric dynamics and critical behavior in the Bak-Sneppen model
• Asymptotic fitness distribution in the Bak-Sneppen model of biological evolution with four species
• Absorbing-state phase transitions with extremal dynamics
• Critical behavior of a stochastic anisotropic Bak-Sneppen model