Abstract: In this paper, by using the analysis of qualitative method and bifurcation theory, we investigated the dynamics of the Monod-Haldane type predator-prey system with constant prey harvesting and a single time delay. It is shown that the Hopf bifurcation can occur as the delay τ crosses some critical values. Furthermore, the direction and stability of the Hopf bifurcation are determined by deriving normal form theory and center manifold theorem. Finally, numerical simulations are performed to illustrate the analytical results.

Key words: time delay, Hopf bifurcation, stability, predator-prey system, time delay, Hopf bifurcation, stability