Abstract: By analyzing the position of the root of characteristic equation on the complex plane, we gave the local asymptotic stability and global stability of unique positive equilibrium point of the model and the existence of Hopf bifurcation, and numerically verified the obtained theoretical results by using the MATLAB software package and numerical methods for solving initial value problems of ordinary differential equations.

Key words: delay, prey-predator model, global stability, Hopf bifurcation