留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型

焦建军 陈兰荪

焦建军, 陈兰荪. 捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型[J]. 应用数学和力学, 2007, 28(12): 1502-1512.
引用本文: 焦建军, 陈兰荪. 捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型[J]. 应用数学和力学, 2007, 28(12): 1502-1512.
JIAO Jian-jun, CHEN Lan-sun. Delayed Stage-Structured Predator-Prey Model With Impulsive Perturbations on Predator and Chemical Control on Prey[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1502-1512.
Citation: JIAO Jian-jun, CHEN Lan-sun. Delayed Stage-Structured Predator-Prey Model With Impulsive Perturbations on Predator and Chemical Control on Prey[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1502-1512.

捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型

基金项目: 国家自然科学基金资助项目(10471117);贵州省重点学科资助项目
详细信息
    作者简介:

    焦建军(1973- ),男,湖南邵阳人,讲师,博士(联系人.Tel:+86-851-8193240;E-mail:jiaojianjun05@126.com).

  • 中图分类号: O175.2;O175.6

Delayed Stage-Structured Predator-Prey Model With Impulsive Perturbations on Predator and Chemical Control on Prey

  • 摘要: 讨论了与害虫治理相关的一类捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型,得到了害虫灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界.得出的结论为现实的害虫治理提供了可靠的策略依据.
  • [1] Barclay H J. Models for pest control using predator release, habitat management and pesticide release in combineation[J].J Appl Ecol,1982,19(2):337-348. doi: 10.2307/2403471
    [2] Paneyya J C. A mathematical model of periodically pulse chemotherapy: tumor recurrence and metastasis in a competition environment[J].Bull Math Biol,1996,58(3):425-447. doi: 10.1007/BF02460591
    [3] d′Onofrio A. Stability properties of pulse vaccination strategy in SEIR epidemic model[J].Math Biol,2002,179(1):57-72.
    [4] Roberts M G, Kao R R.The dynamics of an infectious disease in a population with birth pulse[J].Math Biol,2002,149:23-36.
    [5] Hethcote H. The mathematics of infectious disease[J].SIAM Review,2002,42(4):599-653.
    [6] DeBach P.Biological Control of Insect Pests and Weeds[M].New York: Rheinhold, 1964.
    [7] DeBach P, Rosen D. Biological Control by Natural Enemies[M]. 2nd ed. Cambridge: Cambridge University Press,1991.
    [8] Freedman H J. Graphical stability, enrichment, and pest control by a natural enemy[J].Math Biosci,1976,31(3/4):207-225. doi: 10.1016/0025-5564(76)90080-8
    [9] Grasman J, Van Herwaarden O A,et al.A two-component model of host-parasitoid interactions: determination of the size of inundative releases of parasitoids in biological pest control[J].Math Biosci,2001,169(2):207-216. doi: 10.1016/S0025-5564(00)00051-1
    [10] Caltagirone L E,Doutt R L. Global behavior of an SEIRS epidemic model with delays,the history of the vedalia beetle importation to California and its impact on the development of biological control[J].Ann Rev Entomol,1989,34:1-16. doi: 10.1146/annurev.en.34.010189.000245
    [11] Freedman H I,Gopalsamy K. Global stability in time-delayed single species dynamics[J].Bull Math Biol,1986,48(5/6):485-492.
    [12] Zaghrout A A S, Attalah S H. Analysis of a model of stage-structured population dynamics growth with time state-dependent time delay[J].Appl Math Comput,1996,77(2):185-194. doi: 10.1016/S0096-3003(95)00212-X
    [13] Aiello W G, Freedman H I. A time-delay model of single-species growth with stage-structure[J].Math Biosci,1990,101(2):139-153. doi: 10.1016/0025-5564(90)90019-U
    [14] Aiello W G.The existence of nonoscillatory solutions to a generalized, nonautonomous,delay logistic equation[J].J Math Anal Appl,1990,149(1):114-123. doi: 10.1016/0022-247X(90)90289-R
    [15] Rosen G.Time delays produced by essential nonlinearity in population growth models[J].Bull Math Biol,1987,49(2):253-255.
    [16] Wangersky P J,Cunningham W J. On time large equations of growth[J].Proc Nat Acad Sci USA,1956,42(9):699-702. doi: 10.1073/pnas.42.9.699
    [17] Fisher M E, Goh B S. Stability results for delay-recruitment models in population dynamics[J].J Math Biol,1984,19:117.
    [18] Wang W. Global behavior of an SEIRS epidemic model with delays[J].Appl Math Letters,2002,15(4):423-428. doi: 10.1016/S0893-9659(01)00153-7
    [19] Xiao Y N, Chen L S. A ratio-depengent predator-prey model with disease in the prey[J].Appl Math Comput,2002,131(2/3):397-414. doi: 10.1016/S0096-3003(01)00156-4
    [20] Xiao Y N, Chen L S.An SIS epidemic model with stage structure and a delay[J].Acta Math Appl,English Series,2002,18(4):607-618. doi: 10.1007/s102550200063
    [21] Xiao Y N, Chen L S,Bosh F V D. Dynamical behavior for stage-structured SIR infectious disease model[J].Nonlinear Analysis:RWA,2002,3(2):175-190. doi: 10.1016/S1468-1218(01)00021-9
    [22] Xiao Y N, Chen L S.On an SIS epidemic model with stage-structure[J].J System Science and Complexity,2003,16(2):275-288.
    [23] Lu Z H, Gang S J,Chen L S. Analysis of an SI epidemic with nonlinear transmission and stage structure[J].Acta Math Science,2003,23(4):440-446.
    [24] Aiello W G, Freedman H I, Wu J. Analysis of a model representing stage-structured population growth with state dependent time delay[J].SIAM, J Appl Math,1992,52(3):855-869. doi: 10.1137/0152048
    [25] Murray J D.Mathematical Biology[M].Berlin, Heidelberg, New York: Springer-Verlag, 1989.
    [26] YANG Kuang. Delay Differential Equation With Application in Population Dynamics[M]. N Y: Academic Press, 1987,67-70.
    [27] Cull P. Global stability for population models[J].Bull Math Biol,1981,43(1):47-58.
    [28] LIU Xian-ning,CHEN Lan-sun. Compex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator[J].Chaos, Soliton and Fractals,2003,16(2):311-320. doi: 10.1016/S0960-0779(02)00408-3
    [29] Lakshmikantham V, Bainov D D, Simeonov P.Theory of Impulsive Differential Equations[M].Singapor: World Scientific, 1989.
    [30] Bainov D, Simeonov P.Impulsive Differential Equations: Periodic Solutions and Applications[M].England:Longman,1993.
  • 加载中
计量
  • 文章访问数:  2932
  • HTML全文浏览量:  142
  • PDF下载量:  612
  • 被引次数: 0
出版历程
  • 收稿日期:  2007-03-15
  • 修回日期:  2007-09-06
  • 刊出日期:  2007-12-15

目录

    /

    返回文章
    返回