Asymptotic behavior of spatially distributed replicator systems

2014/06/22 by Bratus, Alexander S., Novozhilov, Artem S., Posvyanskii, Vladimir P.
#Analysis of PDEs (math.AP) #FOS: Biological sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE)

paper · doi:10.48550/arxiv.1406.5746

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.

Related

• Replicator equations and space
• On the reaction-diffusion replicator systems: Spatial patterns and asymptotic behavior
• Solutions with a bounded support promote permanence of a distributed\n replicator equation
• A note on the replicator equation with explicit space and global\n regulation
• Mathematical Models of Evolution and Replicator Systems Dynamics. Chapter 1: Introduction to Replicator Systems