| 具有脉冲扰动和非单调功能反应的三种群捕食系统的分析 |
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| 引用本文： | 陈以平,谢君辉. 具有脉冲扰动和非单调功能反应的三种群捕食系统的分析[J]. 纯粹数学与应用数学, 2009, 25(2): 332-338 |
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| 作者姓名： | 陈以平 谢君辉 |
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| 作者单位： | 湖北民族学院理学院,湖北,恩施,445000;湖南师范大学数学系,湖南,长沙,410081 |
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| 基金项目： | 湖北省教育厅科研项目，湖北省高等学校优秀中青年团队计划项目 |
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| 摘 要： | 研究一类具有脉冲效应和非单调功能反应的两个捕食者一个食饵害虫控制系统．通过脉冲微分方程的Floquet理论和小幅扰动方法，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．最后，通过数值实例，给出了一简单讨论．
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| 关 键 词： | 两个捕食者一个食饵模型 脉冲作用 灭绝性 持续生存 |
Analysis of a three-species predator-prey system with impulsive perturbations and non-monotonic functional response |
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| CHEN Yi-ping,XIE Jun-hui. Analysis of a three-species predator-prey system with impulsive perturbations and non-monotonic functional response[J]. Pure and Applied Mathematics, 2009, 25(2): 332-338 |
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| Authors: | CHEN Yi-ping XIE Jun-hui |
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| Affiliation: | CHEN Yi-ping1,XIE Jun-hui2 (1.School of Science,Hubei Institute for Nationalities,Enshi 445000,China,2.Department of Mathematics,Hunan Normal University,Changsha 410081,China) |
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| Abstract: | A two-predator one-prey system with impulsive effect and non-monotone functional response for pest control is proposed and analyzed.By using the Floquet theory of impulsive differential equation and small amplitude perturbation skills, 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. Lastly, a brief discussion are given by numerical simulation. |
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| Keywords: | two-predator one-prey system impulsive effect extinction permanence |
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