Properties of the Hopf bifurcation in a delayed predator-prey model with continuous prey harvesting

In this paper we study the properties of the Hopf bifurcations obtained for a delayed predator-prey model with continuous prey harvesting. Considering delay as a parameter, we investigate the effect of delay on the stability of the coexisting equilibrium. It is observed that there are stability switches, and Hopf bifurcation occurs when the delay crosses some critical value τ 0. By applying the normal form theory and the center manifold theorem, the formulae that determine the stability and direction of the bifurcating periodic solutions are established. Numerical simulations are carried out to illustrate different analytical findings. For the considered parameters values, results indicate that the Hopf bifurcation is supercritical and the bifurcating periodic solution is stable.