A predator-prey mathematical model with competitive interaction amongst two species

Abstract

A mathematical model is constructed to study the effect of predation on two competing species in which one of the competing species is a prey to the predator whilst the other species is not under predation.  We assume that all species can move by diffusion and study the spatial structure of the species and obtained conditions for the existence and stability of equilibrium solutions. The results indicate the possibility of a stable coexistence of the three interacting species in form of stable oscillations under the reflecting boundary conditions.  Numerical simulations supported our theoretical predictions.   By utilizing Liapunov-like functions and differential inequalities we were able to establish that the system is dissipative.