Stability analysis and hopf bifurcation of intraguild predation model with holling type II functional response

We study a predator-prey model describing intraguild predation with Holling type II functional response. Carrying capacity of the predator and prey depend on the number of biotic resources that vary with time. The mathematical analysis of our model covers the existence and local stability of equilibrium point and Hopf bifurcation. We found three equilibrium points that may exist that is the extinction of prey point, the extinction of predator point and the interior equilibrium point. The extinction of predator point is always unstable and the other can be stable with certain conditions. Hopf bifurcation occurs around interior equilibirum point. Numerical simulation confirms the theoretical results.