A stage structured predator-prey system with delay dependent parameters

In reality, every action and reaction all take time to take effect in real life problems, and many species go through some distinct life stages as they proceed from birth to death. From this viewpoint, we propose a two-stage predator-prey interaction model with delay dependent parameters. Our work shows that under condition which the positive equilibrium exists, the system is uniformly persistent. Next, we give conditions which are both necessary and sufficient for the global stability of the boundary equilibrium. At last, we prove that under suitable hypotheses the positive steady state is globally asymptotically stable. The paper ends with a brief discussion section.