Asymmetric dynamics and critical behavior in the Bak–Sneppen model

Guilherme J.M. Garcia and Ronald Dickman

Physica A: Statistical Mechanics and its Applications, 2004, vol. 342, issue 3, 516-528

Abstract: We investigate, using mean-field theory and simulation, the effect of asymmetry on the critical behavior and probability density of Bak–Sneppen models. Two kinds of anisotropy are investigated: (i) different numbers of sites to the left and right of the central (minimum) site are updated and (ii) sites to the left and right of the central site are renewed in different ways. Of particular interest is the crossover from symmetric to asymmetric scaling for weakly asymmetric dynamics, and the collapse of data with different numbers of updated sites but the same degree of asymmetry. All non-symmetric rules studied fall, independent of the degree of asymmetry, in the same universality class. Conversely, symmetric variants reproduce the exponents of the original model. Our results confirm the existence of two symmetry-based universality classes for extremal dynamics.

Keywords: Self-organized criticality; Extremal dynamics; Universality class; Bak–Sneppen model; Anisotropy (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:342:y:2004:i:3:p:516-528

DOI: 10.1016/j.physa.2004.04.133

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