The effect of prey refuge on the dynamics of three species food web system

Abstract

In this paper, a mathematical model is proposed to study the effect of prey refuge on the dynamics of three species food web system. The food web comprises of a single prey and two competing predators. The two predators predate their prey following Holling type II functional response. In this work we discussed boundedness of the system, existence condition of the equilibrium points and the Jacobean matrix is obtained by linearization techniques. The local stability of the equilibrium points was discussed by using Routh-Hurwitz criteria and the global stability of the equilibrium points by constructing suitable Lyapunov function. Numerical simulation is conducted to support the analytical result. Finally, the effect of prey refuge on the dynamics of one prey two predator was discussed based on the analytical and numerical simulation results. From the numerical simulations, it is found that the dynamical system is persistent for a small value of the refuge constant. However, an increase in the refuge constant leads to the extinction of one of the predator species.