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

Martin Strugarek (1) , Nicolas Vauchelet (1)

1 LJLL - Laboratoire Jacques-Louis Lions

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.

Mots clés: Reaction-diffusion systems; model reduction; asymptotic analysis: population dynamics 2010 AMS subject classification: 35K57; 92D25

Domaines: Equations aux dérivées partielles [math.AP]

Martin Strugarek, Nicolas Vauchelet. Reduction to a single closed equation for 2 by 2 reaction-diffusion systems of Lotka-Volterra type. 2016. ⟨hal-01264980v1⟩