Stability of a stage structured predator-prey system with delay dependent parameters

We present a two-stage predator-prey model with delay dependent parameters and density regulation. We analyze local stability of the equilibriums, and give conditions which are both necessary and sufficient for the global asymptotical stability of the boundary equilibrium (1, 0). We prove that the system is uniformly persistent if the positive equilibrium exists, and the positive steady state is globally asymptotically stable when it is local asymptotically stable. At last, we compare and contrast the dynamics in the two cases corresponding respectively to the present or absence of mortality among the juveniles. It shows that the stage structure models with delay dependent parameters are more suitable than that with delay independent parameters.