中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (1): 23-26.

• 研究论文 • 上一篇    下一篇

具有脉冲投放益虫生物控制害虫的捕食-食饵模型

程惠东   

  1. (山东科技大学理学院,山东 青岛 266510)
  • 收稿日期:2010-01-11 修回日期:1900-01-01 出版日期:2011-01-25 发布日期:2011-01-25

Stage Structured Predatorprey Model with Impulsive Perturbations on Beneficial Insect and Delay

CHENG Huidong   

  1. (College of Science, Shandong University of Science and Technology, Qingdao 266510,China)
  • Received:2010-01-11 Revised:1900-01-01 Online:2011-01-25 Published:2011-01-25

摘要: 讨论了具有阶段结脉冲时滞HollingII功能反应的捕食模型,其中天敌(益虫)进行人工脉冲周期投放,害虫具有阶段结构及成熟期的时滞现象,并进行了系统的数学及生物方面的研究。首先利用离散动力系统的频闪映射得到了害虫根除周期解的存在性,并且利用脉冲及时滞微分方程的基本知识证明了该害虫根除周期解的唯一性和全局吸引性。进一步证明了当天敌的投放量或者投放周期在一定的范围内,能够控制害虫在作物的经济危害水平(EIL)运行的情况下使天敌与害虫可以共存。得出的结论为害虫的生物治理提供了策略基础。

关键词: 脉冲, 阶段结构捕食模型, 时滞, 全局吸引性, 害虫管理

Abstract:

Predatorprey model of a stage structured impulse delay HollingII functional response, in which predator(natural enemy )is released impulsively and the prey has stage structured and maturation time delay are discussed, and a systematic mathematical and ecological study are performed. Using the discrete dynamical system determined by the stroboscopic map, we obtain the existence of pesteradication periodic solution. And show that the pesteradication periodic solution is unique and globally attractive by using the basis of impulse and delay differential equation. Further, we prove that if the pulse releasing rate or impulsive period for natural enemy is within an appropriate range, the pest population can be controlled under the economic injury level(EIL)E, that is, the pest population and the natural enemy population may coexist. The results provide reliable tactical basis for the practical pest management.

Key words: impulse, stage structured predatorprey model, time delays, global attractivity, pest management

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