Fitness noise in the Bak-Sneppen evolution model in high dimensions

TL;DR

This study investigates the spectral properties and critical behavior of the Bak-Sneppen evolution model in higher dimensions, revealing how the noise characteristics and critical dimension relate through finite-size scaling and local activity spectra.

Contribution

It provides new insights into the upper critical dimension of the Bak-Sneppen model by analyzing spectral exponents and local activity in high dimensions, extending previous one-dimensional and mean-field results.

Findings

Spectral exponent approaches mean-field value at D=4

Finite-size scaling confirms the upper critical dimension D=4

Local activity spectra reveal avalanche and return time statistics

Abstract

We study the Bak-Sneppen evolution model on a regular hypercubic lattice in high dimensions. Recent work [Phys. Rev. E 108, 044109 (2023)] has shown the emergence of the $1/f^{\alpha}$ noise for the ``fitness'' observable with $\alpha \approx 1.2$ in one-dimension (1D) and $\alpha \approx 2$ for the random neighbor (mean-field) version of the model. We examine the temporal correlation of fitness in 2, 3, and 4 dimensions. As obtained by finite-size scaling, the spectral exponent tends to take the mean-field value at the upper critical dimension ${\rm D}_u = 4$, which is consistent with previous studies. Our approach provides an alternative way to understand the upper critical dimension of the model. We also show the local activity power spectra, which offer insight into return time statistics and the avalanche dimension.