Hopf Bifurcation in a Delayed Predator-Prey Model with a Holling-Type IV Functional Response

In this paper a delayed predator-prey model system with a Holling-type IV functional response is studied. The bifurcation analysis of the model shows that a sequence of Hopf bifurcations can occur at the coexisting equilibrium as the time delay crosses some critical values. An explicit algorithm for determining the direction of Hopf bifurcations and the stability of bifurcating non-trivial periodic solutions is derived by using normal form theory and center manifold arguments due to Faria and. Finally, numerical simulations are carried out to substantiate our analytical findings.