| We consider a periodic predator-prey system where the prey has a history that takes them through two stages, immature and mature. In this system, immature prey, mature prey and predator are all density-dependent. Immature prey is difficult to be caught because it is little in body form or the environment it lives in is different from the mature. Predator only preys on mature and we assume there are sufficient food sources for prey and predator is a specialist, not a generalist. On the premise of these assumptions, we provide a sufficient and necessary condition to guarantee the permanence of the system.
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