Asymmetric dynamics and critical behavior in the Bak-Sneppen model

TL;DR

This paper explores how asymmetry influences the critical behavior of the Bak-Sneppen model, revealing two universality classes based on symmetry in extremal dynamics through theoretical and simulation methods.

Contribution

It demonstrates that asymmetric rules lead to a distinct universality class from symmetric ones, expanding understanding of critical phenomena in extremal models.

Findings

Asymmetric rules fall into a single universality class regardless of asymmetry degree.

Symmetric variants reproduce original model exponents.

Crossover behavior observed from symmetric to asymmetric scaling.

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.