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Asymmetric dynamics and critical behavior in the Bak–Sneppen model

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  • Garcia, Guilherme J.M.
  • Dickman, Ronald

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.

Suggested Citation

  • Garcia, Guilherme J.M. & Dickman, Ronald, 2004. "Asymmetric dynamics and critical behavior in the Bak–Sneppen model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(3), pages 516-528.
    • Handle: RePEc:eee:phsmap:v:342:y:2004:i:3:p:516-528
    DOI: 10.1016/j.physa.2004.04.133
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    1. Peter Eggert & Eberhard Wettig, 1995. "Die osteuropäischen Länder als Produzenten, Verbraucher und Exporteure von Mangan, Chrom, Nickel und Molybdän," DIW Wochenbericht, DIW Berlin, German Institute for Economic Research, vol. 62(6), pages 154-160.
    2. Eberhard Wettig, 1994. "Die Stellung der UdSSR und ihrer Nachfolgestaaten auf den Weltmärkten ausgewählter Stahlveredler," DIW Wochenbericht, DIW Berlin, German Institute for Economic Research, vol. 61(28), pages 480-483.
    3. Vendruscolo, Michele, 1998. "Protein stability and foldability–designability complementarity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 249(1), pages 576-580.
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