Critical values in Bak-Sneppen type models

TL;DR

This paper calculates critical fitness thresholds in Bak-Sneppen models under various modifications, including non-uniform updates, random neighbors, and binary fitness, providing exact results for these variants.

Contribution

It extends the understanding of critical values in Bak-Sneppen models by analyzing models with altered update rules and neighbor structures, deriving exact thresholds.

Findings

Exact critical values for models with non-uniform updates

Critical thresholds for models with random neighbors

Results for models with binary fitness values

Abstract

In the Bak-Sneppen model, the lowest fitness particle and its two nearest neighbors are renewed at each temporal step with a uniform (0,1) fitness distribution. The model presents a critical value that depends on the interaction criteria (two nearest neighbors) and on the update procedure (uniform). Here we calculate the critical value for models where one or both properties are changed. We study models with non-uniform updates, models with random neighbors and models with binary fitness and obtain exact results for the average fitness and for $p_c$.