Zhang Yujuan, Liu Bing, Chen Lansun
Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, Peoples' Republic of China.
Math Med Biol. 2003 Dec;20(4):309-25. doi: 10.1093/imammb/20.4.309.
In this paper, we investigate a two-prey one-predator system with impulsive effect on the predator of fixed moment. By using Floquet's theorem and small-amplitude perturbation skills, we show that there exists a globally asymptotically stable two-pest eradication periodic solution when the impulsive period is less than some critical value. Further, we prove that the system is permanent if the impulsive period is larger than some critical value, and meanwhile the conditions for the extinction of one of the two prey and permanence of the remaining two species are given. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level. Therefore, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels.
在本文中，我们研究了一个具有固定时刻脉冲效应的两食饵一捕食者系统。通过使用弗洛凯定理和小振幅扰动技巧，我们表明当脉冲周期小于某个临界值时，存在一个全局渐近稳定的双害虫根除周期解。进一步地，我们证明当脉冲周期大于某个临界值时，该系统是持久的，同时给出了两个食饵之一灭绝以及其余两个物种持久存在的条件。最后，数值模拟表明存在一个最大值不超过给定水平的稳定正周期解。因此，我们可以利用正周期解的稳定性及其周期将害虫控制在可接受的低水平。
