LAUSR

Abstract In this paper, spreading properties of a competition-diffusion system of two equations are studied. 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.