Asymptotic behavior of spatially distributed replicator systems

TL;DR

This paper investigates the stability of spatially distributed replicator systems, establishing conditions for biological stability and demonstrating that spatial distribution can stabilize systems that are unstable in non-distributed form.

Contribution

It provides new sufficient conditions for biological stability in reaction-diffusion replicator systems and shows that spatial distribution can stabilize otherwise unstable systems.

Findings

Spatial distribution can induce stability in replicator systems.

Sufficient conditions for biological stability are derived.

Numerical examples confirm analytical results.

Abstract

The question of biological stability (permanence) of a replicator reaction-diffusion system is considered. Sufficient conditions of biological stability are found. It is proved that there are situations when biologically unstable non-distributed replicator system becomes biologically stable in the distributed case. Numerical examples illustrate analytical findings. This manuscript is a continuation of arXiv:1308.5631.