On the impulsive controllability and bifurcation of a predator-pest model of IPM

BioSystems

Volumn 93, Issue 3, 2008, Pages 151-171

  Zhang, Hong ^a   Georgescu, Paul ^b   Chen, Lansun ^c  

^a JIANGSU UNIVERSITY   (China)

^b GHEORGHE ASACHI TECHNICAL UNIVERSITY OF IASI   (Romania)

^c INSTITUTE OF APPLIED MATHEMATICS   (China)

Author keywords

Beddington DeAngelis functional response; Economic threshold; Fixed point approach; Impulsive controls; Permanence; Pest eradication periodic solution; Stability analysis; Supercritical bifurcation

Indexed keywords

BIOLOGICAL CONTROL; INTEGRATED PEST MANAGEMENT; MODELING; PERIODICITY; PEST CONTROL; PESTICIDE APPLICATION; PREDATOR-PREY INTERACTION; SPRAY;

ARTICLE; INTEGRATED PEST MANAGEMENT; MATHEMATICAL ANALYSIS; MODEL; PEST CONTROL; PREDATOR; PREDATOR PREY INTERACTION; SIMULATION;

EID: 48049114204     PISSN: 03032647     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.biosystems.2008.03.008     Document Type: Article

References (27)

1. Abrams A., and Ginzburg L.R. The nature of predation: prey dependent, ratio dependent or neither?. Trends Ecol. Evol. 15 (2000) 337-341
2. Arditi R., and Ginzburg L.R. Coupling in predator-prey dynamics: ratio-dependence. J. Theor. Biol. 139 (1989) 311-326
3. Bainov D.D., and Simeonov P.S. Impulsive Differential Equations: Periodic Solutions and Applications (1993), Longman, London
4. Beddington J.R. Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44 (1975) 331-340
5. Chow S.N., and Hale J. Methods of bifurcation theory (1982), Springer Verlag, New York
6. DeAngelis D.L., Goldstein R.A., and O'Neill R.V. A model for tropic interaction. Ecology 56 (1975) 881-892
7. Debach P., and Rosen D. Biological Control by Natural Enemies. 2nd ed (1991), Cambridge University Press, Cambridge
8. Ferron P. Pest Control Using the Fungi Beauveria and Metarhizinm. In: Burges H.D. (Ed). Microbial Control in Pests and Plant Diseases (1981), Academic Press, London
9. Freedman H.J. Graphical stability, enrichment, and pest control by a natural enemy. Math. Biosci. 31 (1976) 207-225
10. Georgescu, P., Zhang, H., Chen, L.S., 2008. Bifurcation of nontrivial periodic solutions for an impulsively controlled pest management model. Appl. Math. Comput., doi:10.1016/j.amc.2008.03.012.
11. Gutierrez A.P. The physiological basis of ratio-dependent predator-prey theory: a metabolic pool model of Nicholsons blowflies as an example. Ecology 73 (1992) 1552-1563
12. Huisman C., and DeBoer R.J. A formal derivation of the Beddington functional response. J. Theor. Biol. 185 (1997) 389-400
13. Jost C., and Ellner S. Testing for predator dependence in predator-prey dynamics: a nonparametric approach. Proc. Roy. Soc. Lond. B 267 (2000) 1611-1620
14. Kuang Y., and Beretta E. Global qualitative analysis of a ratio-dependent predator-prey system. J. Math. Biol. 36 (1998) 389-406
15. Lakmeche A., and Arino O. Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment. Dyn. Cont., Discrete Impuls. Syst. 7 (2000) 265-287
16. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
17. Liu B., Chen L.S., and Zhang Y.J. The dynamics of a prey-dependent consumption model concerning impulsive control strategy. Appl. Math. Comp. 169 (2005) 305-320
18. Liu B., Zhi Y., and Chen L.S. The dynamics of a predator-prey model with Ivlevs functional response concerning integrated pest management. Acta Math. Appl. Sin. Engl. 20 (2004) 133-146
19. Liu S., and Beretta E. A stage-structured predator-prey model of Beddington-DeAngelis type. SIAM J. Appl. Math. 66 (2006) 1101-1129
20. Luff M.L. The potential of predators for pest control. Agric. Ecos. Environ. 10 (1983) 159-181
21. Skalski G.T., and Gilliam J.F. Functional responses with predator interference: viable alternatives to the Holling type II model. Ecology 82 (2001) 3083-3092
22. Stern V.M., Smith R.F., Van den Bosch R., and Hagen K.S. The integrated control concept. Hilgardia 29 (1959) 81-101
23. Tang S.Y., and Chen L.S. Modelling and analysis of integrated pest management strategy. Discrete Cont. Dyn. Syst. B 4 (2004) 759-768
24. Van den Bosch R. The Pesticide Conspiracy (1978), Doubleday & Co, Garden City, New York
25. Zhang H., Chen L.S., and Georgescu P. Impulsive control strategies for pest management. J. Biol. Syst. 15 (2007) 235-260
26. Zhang H., Jiao J.J., and Chen L.S. Pest management through continuous and impulsive control strategies. BioSystems 90 (2007) 350-361
27. Zhang Y., Liu B., and Chen L.S. Dynamical behavior of Volterra model with mutual interference concerning IPM. ESAIM Math. Mod. Numer. Anal. 38 (2004) 143-155