A delayed stage-structured Holling II predator-prey model with mutual interference and impulsive perturbations on predator

Chaos, Solitons and Fractals

Volumn 40, Issue 4, 2009, Pages 1946-1955

  Jiao, Jianjun ^a   Chen, Lansun ^b   Cai, Shaohong ^a  

^a GUIZHOU UNIVERSITY OF FINANCE AND ECONOMICS   (China)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ECOLOGY;

GLOBAL ATTRACTIVITY; IMPULSIVE PERTURBATIONS; MUTUAL INTERFERENCE; PERIODIC SOLUTION; PEST MANAGEMENT; PREDATOR-PREY MODELING; STAGE STRUCTURED; UNIFORMLY ULTIMATELY BOUNDED;

PREDATOR PREY SYSTEMS;

EID: 65449126353     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.09.074     Document Type: Article

References (31)

1. Lakshmikantham V., Bainov D.D., and Simeonov P. Theory of impulsive differential equations (1989), World Scientific, Singapore
2. Bainov D., and Simeonov P. Impulsive differential equations: periodic solutions and applications vol. 66 (1993), Longman
3. Barclay H.J. Models for pest control using predator release, habitat management and pesticide release in combination. J Appl Ecol 19 (1982) 337-348
4. Paneyya J.C. A mathematical model of periodically pulse chemotherapy: tumor recurrence and metastasis in a competition environment. Bull Math Biol 58 (1996) 425-447
5. d'Onofrio A. Stability properties of pulse vaccination strategy in SEIR epidemic model. Math Biol 179 (2002) 57-72
6. Roberts M.G., and Kao R.R. The dynamics of an infectious disease in a population with birth pulse. Math Biol 149 (2002) 23-36
7. Hui J., and Zhu D. Dynamic complexities for prey-dependent consumption integrated pest management models with impulsive effects. Chaos, Solitons & Fractals 29 1 (2006) 233-251
8. Xiao Y.N., and Chen L.S. An SIS epidemic model with stage structure and a delay. Acta Math Appl Engl Ser 16 (2002) 607-618
9. Gao S., and Chen L. Dynamic complexities in a single-species discrete population model with stage structure and birth pulses. Chaos, Solitons & Fractals 24 4 (2005) 1013-1023
10. Xiao Y.N., and Chen L.S. On an SIS epidemic model with stage-structure. J Syst Sci Complex 16 (2003) 275-288
11. Liu Z., and Tan R. Impulsive harvesting and stocking in a MonodCHaldane functional response predatorCprey system. Chaos, Solitons & Fractals 34 2 (2007) 454-464
12. Hethcote H. The mathematics of infectious disease. SIAM Rev 42 (2002) 599-653
13. Zaghrout A.A.S., and Attalah S.H. Analysis of a model of stage-structured population dynamics growth with time state-dependent time delay. Appl Math Comput 77 (1996)
14. Aiello W.G., Freedman H.I., and Wu J. Analysis of a model representing stage-structured population growth with state dependent time delay. SIAM J Appl Math 52 3 (1992)
15. Murray J.D. Mathematical biology (1989), Springer-Verlag, Berlin Heidelberg (NY)
16. Aiello W.G., and Freedman H.I. A time-delay model of single-species growth with stage-structured. Math Biosci 101 (1990) 139
17. Aiello W.G. The existence of nonoscillatory solutions to a generalized, nonautonomous, delay logistic equation. J Math Anal Appl 149 (1990) 114
18. Freedman H.I., and Gopalsamy K. Global stability in time-delayed single species dynamics. Bull Math Biol 48 (1986) 485
19. Rosen G. Time delays produced by essential nonlinearity in population growth models. Bull Math Biol 49 (1987) 253
20. Wangersky P.J., and Cunningham W.J. On time large equations of growth. Proc Nat Acad Sci USA 42 (1956) 699
21. Fisher M.E., and Goh B.S. Stability results for delay-recruitment models in population dynamics. J Math Biol 19 (1984) 117
22. Yang K. Delay differential equation with application in population dynamics (1987), Academic Press, NY p. 67-70
23. Cull P. Global stability for population models. Bull Math Biol 43 (1981) 47-58
24. Jiao J., Meng X., and Chen L. Global attractivity and permanence of a stage-structured pest management SI model with time delay and diseased pest impulsive transmission. Chaos, Solitons & Fractals 38 3 (2008) 658-668
25. DeBach P. Biological control of insect pests and weeds (1964), Rheinhold, New York
26. DeBach P., and Rosen D. Biological control by natural enemies. 2nd ed. (1991), Cambridge University Press, Cambrige
27. Freedman H.J. Graphical stability, enrichment, and pest control by a natural enemy. Math Biosci 31 (1976) 207-225
28. 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. Math Biosci 169 (2001) 207-216
29. Caltagirone L.E., and 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. Ann Rev Entomol 34 (1989) 1-16
30. Liu X., and Chen L. Compex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator. Chaos, Solitons & Fractals 16 (2003) 311-320
31. Liu B., Zhang Y.J., and Chen L.S. Dynamical behavior of a Lotka-Volterra predator-prey model concerning integrated pest management. Chaos, Solitons & Fractals 6 (2004) 123-134