Effect of Exotic Species on a System of Native Prey-Predator Populations : A Model

Abstract

In this paper, a mathematical model is proposed to study the effect of exotic predator population on a system of native prey-predator population. The model includes three state variables viz., density of native prey, density of native predator and density of exotic predator. The stability analysis of all the feasible equilibria are carried out and also the possibility of Hopf- bifurcation of the interior equilibrium point is investigated for the parameter <img src=image/10.5923.j.ajcam.20120206.07_001.gif></img>; the predation rate of exotic predator. By varying the parameter <img src=image/10.5923.j.ajcam.20120206.07_002.gif></img>, a change in stability behaviour of the interior equilibrium is also observed. The stability and direction of bifurcating periodic solution is discussed. Finally the analytical results are supported by numerical simulation.