Critical behavior of a stochastic anisotropic Bak-Sneppen model

TL;DR

This study investigates the critical behavior of a stochastic anisotropic Bak-Sneppen model, revealing that models with nonzero interaction strength exhibit self-organized criticality and share universal critical exponents.

Contribution

The paper introduces a parameter for interaction strength in the Bak-Sneppen model and analyzes its critical behavior through numerical and simulation methods.

Findings

Models with nonzero interaction strength exhibit self-organized criticality.

Critical exponents are consistent across models, indicating a shared universality class.

Numerical results agree with Monte Carlo simulations.

Abstract

In this paper we present our study on the critical behavior of a stochastic anisotropic Bak-Sneppen (saBS) model, in which a parameter $\alpha$ is introduced to describe the interaction strength among nearest species. We estimate the threshold fitness $f_c$ and the critical exponent $\tau_r$ by numerically integrating a master equation for the distribution of avalanche spatial sizes. Other critical exponents are then evaluated from previously known scaling relations. The numerical results are in good agreement with the counterparts yielded by the Monte Carlo simulations. Our results indicate that all saBS models with nonzero interaction strength exhibit self-organized criticality, and fall into the same universality class, by sharing the universal critical exponents.