A stage structured predator-prey model with time delays

In this paper, a stage structured predator-prey system with two time delays (maturation delay and gestation delay) is studied. Qualitative analysis of the model such as the stability of equilibria and Hopf bifurcation is provided. By using an iterative technique and comparison arguments, sufficient conditions are derived for the global asymptotical stability of the positive equilibrium and the boundary equilibrium of the model. The special case where one of the delays can be ignored is considered, and sufficient conditions are obtained for the occurrence of a Hopf bifurcation of periodic solutions when the gestation delay is varied. It is also shown that varying the maturation delay does not affect the stability of the positive equilibrium.