Reduction to a single closed equation for 2 by 2 reaction-diffusion systems of Lotka-Volterra type
Analysis of PDEs
2016-02-04 v2
Abstract
We consider general models of coupled reaction-diffusion systems for interacting variants of the same species. When the total population becomes large with intensive competition, we prove that the frequencies (i.e. proportions) of the variants can be approached by the solution of a simpler reaction-diffusion system, through a singular limit method and a relative compactness argument. As an example of application, we retrieve the classical bistable equation for Wolbachia's spread into an arthropod population from a system modeling interaction between infected and uninfected individuals.
Keywords
Cite
@article{arxiv.1602.01058,
title = {Reduction to a single closed equation for 2 by 2 reaction-diffusion systems of Lotka-Volterra type},
author = {Martin Strugarek and Nicolas Vauchelet},
journal= {arXiv preprint arXiv:1602.01058},
year = {2016}
}