The dynamics of a stage-structured predator-prey system with impulsive effect and Holling mass defence

Applied Mathematical Modelling

Volumn 36, Issue 1, 2012, Pages 87-96

  Huang, Can Yun ^a   Li, Yan Juan ^a   Huo, Hai Feng ^a  

^a LANZHOU UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Global attractivity; Impulsive effect; Permanence; Stage structure

Indexed keywords

COMPARISON THEOREM; GLOBAL ATTRACTIVITY; IMPULSIVE EFFECTS; PERIODIC SOLUTION; PERMANENCE; PREDATOR - PREY SYSTEM; PREDATOR-PREY MODELS; STAGE STRUCTURE; STROBOSCOPIC TECHNIQUES; SUFFICIENT CONDITIONS; THEORETICAL RESULT;

NUMERICAL ANALYSIS;

EID: 80051824640     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2011.05.038     Document Type: Article

References (36)

1. Clark C.W. Mathematical Bioeconomics 1990, Wiley, New York.
2. Jiang X.W., Song Q., Hao M.Y. Dynamics behaviors of a delayed stage-structured predator-prey model with impulsive effect. Appl. Math. Comput. 2010, 215:4221-4229.
3. Coltman D.W., Donoghue P.O., Jorgenson J.T., Hogg J.T., Strobeck C., Festa-Bianchet M. Undesirable evolutionary consequences of trophy hunting. Nature 2003, 426(6967):655-658.
4. Conover D.O., Munch S.B. Sustaining fisheries yields over evolutionary time scales. Science 2002, 297(5578):94-96.
5. Haugen T., Volestad L.A. A century of life-history evolution in Grayling. Genetica 2001, 112-113:475-491.
6. Heino M., Gods O.R. Fisheries-induced selection pressures in the context of sustainable fisheries. Bull. Mar. Sci. 2002, 70:639-656.
7. Ling L., Wang W.M. Dynamics of a Ivlev-type predator-prey system with constant rate harvesting. Chaos Soliton Fract. 2009, 41:2139-2153.
8. Olsen E.M., Heino M., Lilly G.R., Morgan M.J., Brattey J., Ernande B., Dieckmann U. Maturation trends indicative of rapid evolution preceded the collapse of Northern Cod. Nature 2004, 428:932-935.
9. Hui J., Zhu D. Dynamic complexities for prey-dependent consumption integrated pest management models with impulsive effects. Chaos Soliton Fract. 2006, 29:233-251.
10. Liu B., Chen L.S. The periodic competing Lotka-Volterra model with impulsive effect. IMA J. Math. Med. Biol. 2004, 21:129-145.
11. Liu B., Zhang Y., Chen L.S. The dynamical behaviors of a Lotka-Volterra predator-prey model concerning integrated pest management. Nonlinear Anal. RWA 2005, 6:227-243.
12. D'Onofrio A. Pulse vaccination strategy in the SIR epidemic model: global asymptotic stable eradication in presence of vaccine failures. Math. Comput. Model. 2002, 36:473-489.
13. Zhang H., Georgescu P., Chen L.S. An impulsive predator-prey system with Beddington-Deangelis functional response and time delay. Int. J. Biomath. 2008, 1:1-17.
14. Aiello W.G., Freedman H.I. A time-delay model of single-species growth with stage structure. Math. Biosci. 1990, 101:139-153.
15. Chen F.D., You M.S. Permanence, extinction and periodic solution of the predator-prey system with Beddington-DeAngelis functional response and stage structure for prey. Nonlinear Anal. RWA 2008, 9:207-221.
16. Freedman H.I., Gopalsamy K. Global stability in time-delayed single species dynamics. Bull. Math. Biol. 1986, 48:485-492.
17. Gourley S.A., Kuang Y. A stage structured predator-prey model and its dependence on maturation delay and death rate. J. Math. Biol. 2004, 49:188-200.
18. Song X.Y., Chen L.S. Modelling and analysis of a single species system with stage structure and harvesting. Math. Comput. Model. 2002, 36:67-82.
19. Wang X., Wang W., Lin X. Chaotic behavior of a Watt-type predator-prey system with impulsive control strategy. Chaos Soliton Fract. 2008, 37:706-718.
20. Kuang Y. Delay Differential Equation With Application in Population Dynamics 1993, Academic Press, New York.
21. Li Y.K., Kuang Y. Periodic solutions of periodic delay Lotka-Volterra equations and systems. J. Math. Anal. Appl. 2001, 255:260-280.
22. Holmes J.C., Bethel W.M. Modification of intermediate host behavior parasites. Zool. J. Linnean Soc. 1972, 51:123-149.
23. Freedman H.I., Wolkowicz G.S.K. Predator-prey systems with group defence: the paradox of enrichment revisited. Bull. Math. Biol. 1986, 48:493-508.
24. Ruan S., Xiao D. Global analysis in a predator-prey system with nonmonotonic functional response. SIAM J. Appl. Math. 2000, 61(4):1445-1472.
25. Zhu H., Campbell S., Wolkowicz G. Bifurcation analysis of a predator-prey system with nonmonotonic functional response. SIAM J. Appl. Math. 2002, 63(2):636-682.
26. Jiao J.J., Meng X.Z., Chen L.S. A stage-structured Holling mass defence predator-prey model with impulsive perturbations on predators. Appl. Math. Comput. 2007, 189:1448-1458.
27. Liu Z.J., Tan R.H. Impulsive harvesting and stocking in a Monod-Haldane functional response predator-prey system. Chaos Soliton Fract. 2007, 34:454-464.
28. Andrews J.F. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnol. Bioeng. 1968, 10:707-723.
29. Jiao J.J., Meng X.Z., Chen L.S. Harvesting policy for a delayed stage-structured Holling II predator-prey model with impulsive stocking prey. Chaos Soliton Fract. 2009, 41:103-112.
30. Jiao J.J., Pang G.P., Chen L.S., Luo G.L. A delayed stage-structured predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Appl. Math. Comput. 2008, 195:316-325.
31. Song X.Y., Hao M.Y., Meng X.Z. A stage-structured predator-prey model with disturbing pulse and time delays. Appl. Math. Model. 2009, 33:211-223.
32. Shao Y., Dai B. The dynamics of an impulsive delay predator-prey model with stage structure and Beddington-type functional response. Nonlinear Anal. RWA 2010, 11:3567-3576.
33. Bainov D., Simeonov P. Impulsive Differential Equations: Periodic Solutions and Applications 1993, Longman.
34. Lakshmikantham V., Bainov D.D., Simeonov P. Theory of Impulsive Differential Equations 1989, World Scientific, Singapore.
35. Bainov D., Simeonov P. System with Impulsive Effect: Stability Theory and Applications 1989, John Wiley and Sons, New York.
36. Song X.Y., Chen L.S. Optimal harvesting and stability for a two species competitive system with stage structure. Math. Biosci. 2001, 170:173-186.