食饵具脉冲扰动与捕食者具连续收获的时滞捕食-食饵模型的动力学行为

摘要

运用时滞泛函微分方程的基本理论和脉冲微分方程的比较定理、周期解存在定理,研究一个食饵具脉冲扰动与捕食者具连续收获的时滞捕食一食饵模型,得到捕食者灭绝周期解的全局吸引和系统持久的充分条件,证明系统所有解的一致完全有界.所得的结论可以为现实的生物资源管理提供策略依据.%A delayed predator-prey model with impulsive perturbations on prey and continuous harvesting on predator is studied. By using basic theory of delay differential equation, comparison theorem and periodic solution existing theorem of impulsive differential equations, sufficient conditions which guarantee the global attraction of predator-extinction periodic solution and permanence of the system are obtained. It is also proved that all solutions of the system are uniformly and ultimately bounded. The results provide reliable tactic basis for the practical biological resource management and enrich the theory of impulsive differential equation.