Abstract: Using the Hopf bifurcation theory, we studied a class of Leslie-Gower predator-prey models with time delay. Firstly, taking time delay as the bifurcation parameter, we discussed the stability of the positive equilibrium point of the model and the existence of Hopf bifurcation. Secondly, according to the normal form theory and center manifold theorem for partial differential equation, we derived the direction of Hopf bifurcation and the stability of bifurcation periodic solutions. Finally, we used MATLAB for numerical simulations.

Key words: time delay, Leslie-Gower model, Hopf bifurcation, stability