Asymptotic Dynamics of a Three-Species Hybrid Competition System

We study the dynamics of the classical solutions of a three-species hybrid competition system in a spatially heterogeneous environment. The species compete for resources using different strategies: the first species disperses nonlocally, the second locally, whereas the third does not disperse. When the environment has a sink area, we show that the non-dispersing species wins the competition, driving the others to extinction. However, in the absence of a sink area, all the species coexist, and there is a continuum of positive coexistence steady states. We also examine the dynamics of the classical solutions of a consumer-resource system comprising a non-dispersing single resource species whose density function evolves and is consumed by three competitors in a hybrid competition model. In this case, we also show that when the habitat has a sink area, the competition favors the non-dispersing species. However, all the competitors coexist when there is no sink area.