Fitness Fluctuations and Correlation Time Scaling in the Barycentric Bak-Sneppen Model

TL;DR

This study analyzes the barycentric Bak-Sneppen model, revealing long-range correlations and power-law scaling in fitness fluctuations and cover time, with implications for understanding self-organized criticality in complex systems.

Contribution

It introduces a barycentric version of the Bak-Sneppen model and characterizes its critical exponents, spectral density, and cover time distribution using numerical and statistical methods.

Findings

Power spectral density follows 1/f^α with 0<α<2.

Cover time scales as a power law with system size.

Distribution of cover time fits generalized extreme value distribution.

Abstract

We consider the barycentric version of the Bak-Sneppen model, a one-dimensional self-organized critical model that describes generalized Keynesian beauty contests with a local interaction rule. We numerically investigate the power spectral density of the fitness variable and correlation time. Through data collapse for both variables, we estimate the critical exponents. For global and local fitness variables, the power spectral density exhibits $1/f^{\alpha}$ with $0< \alpha < 2$, indicative of long-range correlations. We also investigate the cover time, defined as the duration required for the extinction or mutation of species across the entire system in the critical state of the barycentric BS model. Using finite-size scaling and extreme value theory, we analyze the statistical properties of the cover time. Our results show power-law scaling with system size for the mean, variance, mode, and peak probability. Furthermore, the cumulative probability distribution exhibits data collapse, and the associated scaling function is well described by the generalized extreme value density, closely approximating the Gumbel family.