Damage spreading in the Bak-Sneppen model: Sensitivity to the initial conditions and equilibration dynamics

TL;DR

This paper studies the sensitivity and relaxation dynamics of the Bak-Sneppen model of biological evolution using damage spreading, revealing power-law growth, exponential relaxation, and links to nonextensive statistical mechanics.

Contribution

It introduces a proper Hamming distance measure to analyze damage spreading and characterizes the model's dynamics across different time regimes with a unified framework.

Findings

Initial power-law growth of damage in finite systems

Exponential relaxation towards equilibrium

Connection to nonextensive statistical mechanics

Abstract

The short-time and long-time dynamics of the Bak-Sneppen model of biological evolution are investigated using the damage spreading technique. By defining a proper Hamming distance measure, we are able to make it exhibits an initial power-law growth which, for finite size systems, is followed by a decay towards equilibrium. In this sense, the dynamics of self-organized critical states is shown to be similar to the one observed at the usual critical point of continuous phase-transitions and at the onset of chaos of non-linear low-dimensional dynamical maps. The transient, pre-asymptotic and asymptotic exponential relaxation of the Hamming distance between two initially uncorrelated equilibrium configurations is also shown to be fitted within a single mathematical framework. A connection with nonextensive statistical mechanics is exhibited.