具有时滞和阶段结构的捕食系统的持久性与周期性

摘要

研究一类具有阶段结构和时滞的捕食系统.在此系统中,考虑食饵种群具有幼年和成年两个生长阶段.幼年食饵由它们的父母喂养,不需外出觅食,从而捕食者对它们的攻击可以忽略不计.并且考虑捕食种群的增长受消化时滞的影响.利用一些引理和比较定理探讨了该系统在一定条件下的持久性和周期性.%A periodic predator-prey system with time delay and stage structure is investigated. It is assumed that the prey population has two stages, immature and mature, and that the immature are hidden and raised by their parents. Then the rate of the predator attacking at the immature prey is ignored. Furthermore, the growth of the predator is affected by the time delay due to gestation. By some Lemmas and the vector comparison theorem, the conditions for the permanence and existence of positive periodic solutions of the system are obtained.