Séminaire EDP, Modélisation et Calcul Scientifique (commun ICJ & UMPA)

Vitesses de propagation d'un système de compétition-diffusion à deux espèces

par Cécile Carrère (Université Pierre et Marie Curie)

salle Fokko du Cloux (ICJ, UCBL - La Doua, Bât. Braconnier)

salle Fokko du Cloux

ICJ, UCBL - La Doua, Bât. Braconnier

We consider spreading properties of a competition-diffusion system of two equations. This system models the invasion of an empty favorable habitat, by two competing species, each obeying a logistic growth equation, such that any coexistence state is unstable. If the two species are initially absent from the right half-line x > 0, and the slowest one dominates the fastest one on x < 0, then the latter will invade the right space at its Fisher- KPP speed, and will be replaced by or will invade the former, depending on the parameters, at a slower speed. Thus, the system forms a propagating terrace, linking an unstable state to two consecutive stable states.
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