Dynamics of a Ivlev-type predator–prey system with constant rate harvesting

In this paper, by using the analysis of qualitative method and bifurcation theory, we investigate the dynamical properties of the Ivlev-type predator–prey model with nonzero constant prey harvesting and with or without time delay, respectively. It is shown that the system we considered can exhibit the subcritical and supercritical Hopf bifurcation. We also study the effect of the time delay on the dynamics of the system. By choosing the delay s as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay s crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhães. Finally, numerical simulations are performed to illustrate the obtained results.