A model for the allelopathic effect on two competing species

Abstract

In this paper, a mathematical model is proposed and analysed to study the coexistence of two competing plant species in a finite habitat by assuming that each species produces a toxic substance affecting the other species. The diffusion of toxic substances is also considered in the model. It is shown that the usual existence criteria between two competing species in the absence of toxicant may be changed if each species produces toxicant in large amount affecting the other. In case of no diffusion criteria for local stability, instability and global stability of the system are obtained. In case of allelopathy, where one species produces toxicant and affects the other, it is found that the affected species may be driven to extinction. It is also found that diffusion has a stabilizing effect on the system.