On the reaction-diffusion replicator systems: Spatial patterns and asymptotic behavior

TL;DR

This paper reviews analytical methods for incorporating spatial variables into replicator equations, highlighting how spatial patterns emerge in reaction-diffusion systems relevant to mathematical biology.

Contribution

It provides a concise overview of approaches to include spatial structure in replicator systems and discusses the emergence of spatial patterns.

Findings

Spatial patterns can form in reaction-diffusion replicator systems.

Analytical methods help understand the asymptotic behavior of these systems.

The review summarizes key results on pattern formation.

Abstract

The replicator equation is ubiquitous for many areas of mathematical biology. One of major shortcomings of this equation is that it does not allow for an explicit spatial structure. Here we review analytical approaches to include spatial variables to the system. We also provide a concise exposition of the results concerning the appearance of spatial patterns in replicator reaction-diffusion systems.