Simple model of self-organized biological evolution as completely integrable dissipative system

TL;DR

This paper presents a novel representation of the Bak-Sneppen model of biological evolution as a completely integrable dissipative system, highlighting its self-organized criticality through an integrable framework.

Contribution

It introduces a new integrable systems perspective to the Bak-Sneppen model, connecting biological evolution with mathematical physics.

Findings

Representation of the Bak-Sneppen model as an integrable system

Identification of variables as analogs to integrals of motion

Insight into the temporal influence and exclusion of variables in evolution

Abstract

The Bak-Sneppen model of self-organized biological evolution of an infinite ecosystem of randomly interacting species is represented in terms of an infinite set of variables which can be considered as an analog to the set of integrals of motion of completely integrable system. Each of this variables remains to be constant but its influence on the evolution process is restricted in time and after definite moment its value is excluded from description of the system dynamics.