1/f-noise in the Bak-Sneppen model

TL;DR

This paper investigates the Bak-Sneppen model's self-organized criticality by analyzing time correlation functions, revealing a universal 1/f power spectrum in both analytical and numerical cases.

Contribution

It provides analytical results for the random neighbor version and numerical analysis for the 1D lattice, demonstrating 1/f noise in the model's correlation functions.

Findings

Power spectrum exhibits 1/f behaviour in both model variants.

Analytical results obtained for the random neighbor case.

Numerical results support 1/f noise in the 1D lattice.

Abstract

We calculate time correlation functions in the Bak-Sneppen model (Phys. Rev. Lett. {\bf 71} 4083 (1993)), a model showing self-organised criticality. For a random neighbour version of the model, analytical results are presented, while on a one dimensional lattice we give numerical results. The power spectrum of these correlation functions shows $1/f$- behaviour in both cases.