Convergence dynamics of 2-dimensional isotropic and anisotropic Bak-Sneppen models

TL;DR

This paper investigates the convergence dynamics of 2D isotropic and anisotropic Bak-Sneppen models using a minimum difference technique, revealing scale-invariant intermittent displacement behaviors in their evolution.

Contribution

It introduces a novel application of the minimum difference method to analyze convergence in 2D Bak-Sneppen models, extending previous 1D studies.

Findings

Displacement evolution is intermittent in both models.

Scaling laws indicate absence of characteristic spatial-temporal scales.

Results suggest scale-invariant convergence dynamics.

Abstract

The conventional Hamming distance measurement captures only the short-time dynamics of the displacement between the uncorrelated random configurations. The minimum difference technique introduced by Tirnakli and Lyra [Int. J. Mod. Phys. C 14, 805 (2003)] is used to study the short-time and long-time dynamics of the two distinct random configurations of the isotropic and anisotropic Bak-Sneppen models on a square lattice. Similar to 1-dimensional case, the time evolution of the displacement is intermittent. The scaling behavior of the jump activity rate and waiting time distribution reveal the absence of typical spatial-temporal scales in the mechanism of displacement jumps used to quantify the convergence dynamics.