Dynamic behavior of a class of predator-prey model with two time delays

Abstract

In this paper, three modified Lesile-Gower predator-prey models with two time delays are considered. Taking the time delay as bifurcation parameter, when Hopf bifurcation occurs, the critical value corresponding to time delay is obtained. By using normal form theory and central manifold argument, the direction of Hopf bifurcation and the stability of bifurcation periodic solution can be determined. Finally, numerical simulation is performed to support theoretical analysis.