A new hierarchy of avalanches observed in Bak-Sneppen evolution model

TL;DR

This paper introduces a new measure called average fitness in the Bak-Sneppen model, revealing a novel hierarchy of avalanches and providing exact threshold calculations, enhancing understanding of self-organized criticality.

Contribution

The paper presents a new quantity for the Bak-Sneppen model, derives an exact gap equation, and identifies critical exponents through simulations, advancing the analysis of self-organized criticality.

Findings

New hierarchy of avalanches observed

Exact threshold of the new quantity determined

Avalanche exponents estimated from simulations

Abstract

A new quantity, average fitness, is introduced in Bak-Sneppen evolution model. Through this new quantity, a new hierarchy of avalanches is observed in the evolution of Bak-Sneppen model. An exact gap equation, governing the self-organization of the model, is presented. It is found that the self-organized threshold of the new quantity can be exactly obtained. Two basic exponents, avalanche distribution and avalanche dimension are given through simulations of one- and two-dimensional Bak-Sneppen models. It is suggested that this new quantity may be a good quantity in determining the emergence of criticality.