Damage spreading in 2-dimensional isotropic and anisotropic Bak-Sneppen models

TL;DR

This study applies damage spreading analysis to 2D Bak-Sneppen models, revealing power-law sensitivity and finite size scaling behavior at the critical state, with growth exponents influenced by transient time.

Contribution

First numerical investigation of damage spreading in 2D isotropic and anisotropic Bak-Sneppen models, demonstrating critical sensitivity and scaling properties.

Findings

Power-law sensitivity to initial conditions at criticality

Finite size scaling collapse observed for both models

Growth exponent affected by transient time choice

Abstract

We implement the damage spreading technique on 2-dimensional isotropic and anisotropic Bak-Sneppen models. Our extensive numerical simulations show that there exists a power-law sensitivity to the initial conditions at the statistically stationary state (self-organized critical state). Corresponding growth exponent $\alpha$ for the Hamming distance and the dynamical exponent $z$ are calculated. These values allow us to observe a clear data collapse of the finite size scaling for both versions of the Bak-Sneppen model. Moreover, it is shown that the growth exponent of the distance in the isotropic and anisotropic Bak-Sneppen models is strongly affected by the choice of the transient time.