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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 anexplicit spatial structure. Here we review analytical approaches to includespatial variables to the system. We also provide a concise exposition of theresults concerning the appearance of spatial patterns in replicatorreaction-diffusion systems.

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