Effect on persistence of intra-specific competition in competition models

Abstract

An ecological model describing the competition for a single substrate of an arbitrary number of species is considered. The mortality rates of the species are not supposed to have all the same value and the growth function of the substrate is not supposed to be linear or decreasing. Intra-specific competition is taken into account. Under additional technical assumptions, we establish that the model admits a globally asymptotically stable positive equilibrium point. This ensures persistence of the species. Our proof relies on a Lyapunov function.

Keywords

• Species coexistence
• ecology
• population dynamics