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具有脉冲控制的Ivlev型捕食系统的动态行为 被引量：1

Dynamic Behavior of Pluse Controlled Ivlev-typed Predator-prey Model
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摘要 对具有脉冲控制策略的Ivlev型捕食与被捕食系统进行了定性分析.利用Floquet理论和微分方程比较定理证明了当临界值R0<1时,系统的害虫根除周期解是全局渐近稳定的.害虫控制策略中一个最重要的问题是:应该投放多少天敌和喷洒多少次杀虫剂才能有效控制害虫和保护环境.数值模拟分析了喷洒杀虫剂的剂量和次数,天敌和害虫的残存率如何影响临界值,为成功的害虫控制策略提供理论依据. A qualitative analysis is made of the lvlev-typed predator-prey system with impulsive effect. It is proved with the Floquet theory and the differential comparison theory that, when R0〈l, there exists a globally asymptotically stable pest-free periodic solution. One of the the most important problems in the IPM is how many natural enemies should be released and how much pestcide should be sprayed to control the pest population effectively without environmental damage. Through numerical simulation, the paper discusses the dosage and times the pestcide should be sprayed, how the threshould value is affected by the survival nate of the natural enemies and pests. The study is hoped to provide a theoretical underpinning for successful pest control.
作者 李畅通 戴飞 冯孝周
机构地区 西安工业大学理学院
出处 《西安工业大学学报》 CAS 2012年第1期5-8,14,共5页 Journal of Xi’an Technological University
基金 陕西省教育厅科学计划项目(09JK480) 西安工业大学校长基金项目(XAGDJJ0830)
关键词 脉冲作用 全局稳定 周期解 持续生存 impulsive effect global stability periodic solution permanence
分类号 O175 [理学—基础数学]
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参考文献9

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二级参考文献19

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共引文献38

同被引文献9

  • 1LI Y K, KUANG Y. Periodic Solutions of Periodic Delay Lotka- Volterra Equations and Systems[J]. J Math Anal Appl, 2001,255 (1) : 260.
  • 2TANG S Y, TANG G Y, CHEKE R A. Optimum Timing for Integrated Pest Management: Modeling Rates of Pesticide Application and Natural Enemy Releases[J]. Journal of Theoretical Biology, 2010, 264(2) : 623.
  • 3SONG X Y, HAO M Y, MENG X Z. A Stage Structured Predator- Prey Model with Disturbing Pulse and Time Delays[J]. Appl Math Model, 2009, 33(1):211.
  • 4JIAO J J,PANG G P,CHEN L S. A Delayed Stage Structured Predator Prey Model with Impulsive Stocking on Prey and Continuous Harvesting on Predator[J]. Applied Mathematics and Compulation, 2008,195(1) : 316.
  • 5HUANG C Y,LI Y J,HUO H F. The Dynamics of a Stage- Structured Predator- Prey System with Impulsive Effect and Holling Mass Defence[J]. Appl Math Model,2012,36(1) :87.
  • 6SHAO Y, DAI B. The Dynamics of an Impulsive Delay Predator Prey Model with Stage Structure and Beddington Type Functional Response[J]. Nonlinear Anal RWA,2010,11 (5) :3567.
  • 7SONG X Y, HAO M Y, MENG X Z. A Stage Structured Predator Prey Model with Disturbing Pulse and Time Delays [J]. Appl Math Model, 2009,33(1) :211.
  • 8CHANGTONG LI,SANYI TANG.THE EFFECTS OF TIMING OF PULSE SPRAYING AND RELEASING PERIODS ON DYNAMICS OF GENERALIZED PREDATOR-PREY MODEL[J].International Journal of Biomathematics,2012,5(1):157-183. 被引量：13
  • 9李畅通.一类具有密度制约的捕食与被捕食系统的定性分析[J].西安工业大学学报,2012,32(7):517-521. 被引量：1

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西安工业大学学报
2012年 第1期

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