Reduction to a single closed equation for 2 by 2 reaction-diffusion systems of Lotka-Volterra type - Archive ouverte HAL Access content directly
Journal Articles SIAM Journal on Applied Mathematics Year : 2016

Reduction to a single closed equation for 2 by 2 reaction-diffusion systems of Lotka-Volterra type

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.
Fichier principal
Vignette du fichier
Reduction_v10.pdf (1.04 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01264980 , version 1 (30-01-2016)
hal-01264980 , version 2 (02-02-2016)

Identifiers

Cite

Martin Strugarek, Nicolas Vauchelet. Reduction to a single closed equation for 2 by 2 reaction-diffusion systems of Lotka-Volterra type. SIAM Journal on Applied Mathematics, 2016, 76 (5), pp.2060-2080. ⟨hal-01264980v2⟩
662 View
236 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More