Local equilibrium in the Bak-Sneppen model

TL;DR

This paper investigates the Bak-Sneppen model's local equilibrium properties with varying neighbor interactions, providing bounds for the critical fitness threshold and enhancing understanding of self-organized criticality.

Contribution

It introduces a local equilibrium relationship for the Bak-Sneppen model with arbitrary neighbor interactions, enabling bounds for the critical fitness value.

Findings

Derived a simple local equilibrium relationship for the model

Established bounds for the critical fitness value $p_{c,m}$

Extended understanding of self-organized criticality in the model

Abstract

The Bak Sneppen (BS) model is a very simple model that exhibits all the richness of self-organized criticality theory. At the thermodynamic limit, the BS model converges to a situation where all particles have a fitness that is uniformly distributed between a critical value $p_c$ and 1. The $p_c$ value is unknown, as are the variables that influence and determine this value. Here, we study the Bak Sneppen model in the case in which the lowest fitness particle interacts with an arbitrary even number of $m$ nearest neighbors. We show that $p_{c,m}$ verifies a simple local equilibrium relationship. Based on this relationship, we can determine bounds for $p_{c,m}$.