$1/f$ noise in extremal dynamics

TL;DR

This paper introduces a variant of the Bak-Sneppen model that exhibits robust $1/f$ noise in global fitness fluctuations, with autocorrelation decaying logarithmically, highlighting universal critical dynamics.

Contribution

A simple Bak-Sneppen variant demonstrating robust $1/f$ noise and logarithmic autocorrelation decay, emphasizing hyper-universality in extremal dynamics.

Findings

Global fitness fluctuations show $1/f^{eta}$ noise with $eta o 1$.

Autocorrelation function decays logarithmically over time.

The $1/f$ noise is robust and hyper-universal across model variants.

Abstract

The Bak-Sneppen (BS) evolution model remains a well-studied example of self-organized criticality (SOC). We propose a simple variant of the BS model, where the global fitness fluctuations show $1/f^{\alpha}$ noise with a spectral exponent nearly equal to 1 (pink noise). To further corroborate, we compute the two-time autocorrelation function that decays logarithmically. The $1/f$ noise in the global fitness is robust and hyper-universal. We identify the dominance of non-trivial local fitness cross-power spectra.