A stage-structured Holling mass defence predator-prey model with impulsive perturbations on predators

Applied Mathematics and Computation

Volumn 189, Issue 2, 2007, Pages 1448-1458

  Jiao, Jianjun ^a,c   Meng, Xinzhu ^b   Chen, Lansun ^c  

^a GUIZHOU UNIVERSITY OF FINANCE AND ECONOMICS   (China)

^b SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Global attractivity; Impulsive; Permanence; Pest extinction; Stage structured; Time delay

Indexed keywords

GLOBAL OPTIMIZATION; PERTURBATION TECHNIQUES; PEST CONTROL; TIME DELAY;

GLOBAL ATTRACTIVITY; PERMANENCE; PEST EXTINCTION; PREDATOR-PREY MODEL;

MATHEMATICAL MODELS;

EID: 34249110754     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.12.043     Document Type: Article

References (29)

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 (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. Xiao Y.N., and Chen L.S. A ratio-dependent predator-prey model with disease in the prey. Appl. Math. Comput. 131 (2002) 397-414
8. Xiao Y.N., and Chen L.S. An SIS epidemic model with stage structure and a delay. Acta Math. Appl. English Series 16 (2002) 607-618
9. Xiao Y.N., Chen L.S., and Bosh F.V.D. Dynamical behavior for stage-structured SIR infectious disease model. Nonlinear Anal.: RWA 3 (2002) 175-190
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. Lu Z.H., Gang S.J., and Chen L.S. Analysis of an SI epidemic with nonlinear transmission and stage structure. Acta Math. Sci. 4 (2003) 440-446
12. 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)
13. 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)
14. Murray J.D. Mathematical Biology (1989), Springer-Verlag, Berlin Heidelberg, New York
15. Aiello W.G., and Freedman H.I. A time-delay model of single-species growth with stage-structured. Math. Biosci. 101 (1990) 139
16. Aiello W.G. The existence of nonoscillatory solutions to a generalized, nonautonomous,delay logistic equation. J. Math. Anal. Appl. 149 (1990) 114
17. Freedman H.I., and Gopalsamy K. Global stability in time-delayed single species dynamics. Bull. Math. Biol. 48 (1986) 485
18. Rosen G. Time delays produced by essential nonlinearity in population growth models. Bull. Math. Biol. 49 (1987) 253
19. Wangersky P.J., and Cunningham W.J. On time large equations of growth. Proc. Nat. Acad. Sci. USA 42 (1956) 699
20. Fisher M.E., and Goh B.S. Stability results for delay-recruitment models in population dynamics. J. Math. Biol. 19 (1984) 117
21. Yang K. Delay Differential Equation with Application in Population Dynamics (1987), Academic Press, NY
22. Cull P. Global stability for population models. Bull. Math. Biol. 43 (1981) 47-58
23. Wang W. Global behavior of an SEIRS epidemic model with delays. Appl. Math. Lett. 15 (2002) 423-428
24. DeBach P. Biological Control of Insect Pests and Weeds (1964), Rheinhold, New York
25. DeBach P., and Rosen D. Biological Control by Natural Enemies. 2nd ed. (1991), Cambridge University Press, Cambrige
26. Freedman H.J. Graphical stability, enrichment, and pest control by a natural enemy. Math. Biosci. 31 (1976) 207-225
27. 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
28. 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
29. Liu X., and Chen L. Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator Chaos. Soliton Fract. 16 (2003) 311-320