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A predator-prey system with a stage structure for the prey. (English) Zbl 1132.92340
Summary: This paper considers a periodic predator-prey system where the prey has a life history that takes the prey through two stages: immature and mature. We provide a sufficient and necessary condition to guarantee permanence of the system. It is shown that the system is permanent if and only if the growth of the predator by foraging the prey minus its death rate is positive on average during the period.
MSC:
92D40Ecology
34C25Periodic solutions of ODE
34D23Global stability of ODE
34D40Ultimate boundedness (MSC2000)
37N25Dynamical systems in biology