Hopf bifurcation and global stability of a delayed predator–prey model with prey harvesting

In this paper, we consider a delayed prey–predator model with modified Leslie–Gower term and Michaelis–Menten type prey harvesting. Regarding time delay as a bifurcation parameter, and using the normal form and center manifold theorem of functional differential equations and partial differential equations, we obtain the existence, stability and direction of periodic solutions of functional differential equations and partial differential equations, respectively. Numerical simulations are carried out to depict our theoretical analysis.