Spreading speed in a non-monotonic Ricker competitive integrodifference system

Abstract

<p style='text-indent:20px;'>This article studies the propagation threshold in a competitive system without the classical comparison principle, which models the invasion-coexistence process between two competitors of which one is the invader and another is the aborigine. We obtain a linearly determined threshold that is the spreading speed of the invader in initial value problems. To estimate the spreading speed, we construct several auxiliary scalar equations and use the method of generalized upper solutions. In population dynamics, our results imply that even in a nonmonotone competitive system, the invader may invade the habitat of the aborigine at an almost constant speed and two species could coexist eventually.</p>