具时滞和脉冲的捕食者-食饵模型的动力学性质

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时滞的第III功能反应的捕食者-食饵脉冲动力系统.证明了当脉冲周期小于某个临界值时,系统存在一个渐进稳定的害虫灭绝周期解,否则系统持续生存.并用Matlab软件对害虫灭绝周期解及害虫周期爆发现象进行了数值模拟.

The Dynamics of Predator-Prey Model with Impulsive and Time Daley

Considering biological control and chemical control strategy and the effects of chemical pesticides on natural enemy,we propose a predator-prey model with III functional response in two different times 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.The question of the nontrivial periodic solution off the round of pest-eradication periodic solution is discussed and the phenomenon of the pest-eradication periodic solution and the periodic outburst of pest are simulated by Matlab.