A Delayed Diffusive Predator-Prey System with Michaelis-Menten Type Predator Harvesting

The predator-prey model is fundamentally important to study the growth law of the population in nature. In this paper, we propose a diffusive predator-prey model, in which we also consider time delay in the gestation time of predator and Michaelis-Menten type predator harvesting. By analyzing the distribution of eigenvalues, we investigate the stability of the coexisting equilibrium and the existence of Hopf bifurcation using time delay as bifurcation parameter. We analyze the property of Hopf bifurcation, and give an explicit formula for determining the direction and the stability of Hopf bifurcation. Finally, some numerical simulations are given to support our results.