基于脉冲扰动作用下的一个捕食者-食饵模型的动力学性质

The Dynamics of a Predator-Prey Model Concerning Impulsive Perturbations

基于害虫的生物控制和化学控制策略,考虑到化学杀虫剂对天敌的影响,利用脉冲微分方程建立了在不同的固定时刻分别喷洒杀虫剂和释放天敌的具有依氏(Ivlev)功能性反应的捕食者-食饵脉冲动力系统．证明了当脉冲周期小于某个临界值时,系统存在一个渐近稳定的害虫根除周期解,否则系统是持续生存的．通过分析表明如果采取有效的化学控制策略,那么这种综害虫合控制策略更有效．

In this paper, considering biological control and chemical control strategy and the effects of chemical pesticides on natural enemy, we propose a predator-prey model with Ivlev＇s functional response by using impulsive differential equation. It is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Otherwise, the system can be permanent. We obtain that our impulsive control strategy is more effective than the classical one if we take chemical control efficiently.