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.

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

  • Received Date: 2007-03-15
  • Rev Recd Date: 2007-09-06
  • Publish Date: 2007-12-15
  • A delayed stage-structured pest management predator-prey system with impulsive transmitting on predators and chemical on prey concern was considered. Sufficient conditions of the global attractivity of pest-extinction boundary periodic solution and permanence of the system were obtained. It was also proved that all solutions of the system are uniformly ultimately bounded. The results provide reliable tactical basis for the practical pest management.
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  • [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.
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