The dynamical behaviors of a Lotka-Volterra predator-prey model concerning integrated pest management

Nonlinear Analysis: Real World Applications

Volumn 6, Issue 2, 2005, Pages 227-243

  Liu, Bing ^a,b   Zhang, Yujuan ^a   Chen, Lansun ^c  

^a ANSHAN NORMAL UNIVERSITY   (China)

^b XINJIANG UNIVERSITY   (China)

^c CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Extinction; Impulsive effect; IPM strategy; Lotka Volterra predator prey model; Permanence

Indexed keywords

ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); DIFFERENTIAL EQUATIONS; LINEARIZATION; MATRIX ALGEBRA; PEST CONTROL; PESTICIDES; THEOREM PROVING;

IMPULSIVE EFFECT; INTEGRATED PEST MANAGEMENT STRATEGY; LOTKA-VOLTERRA PREDATOR-PREY MODEL; PERMANENCE; PEST ERADICATION;

MATHEMATICAL MODELS;

EID: 10244240509     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2004.08.001     Document Type: Article

References (20)

1. Z. Ager, L. Cojocam, R. Anderson,Y. Danon, Pulse mass measles vaccination across age cohorts, Proc. Natl. Acad. Sci. USA 90 (1993) 11698-11702.
2. D. Bainov, P. Simeonov, Impulsive differential equations: periodic solutions and applications, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 66, 1993.
3. H.J. Barclay, Models for pest control using predator release, habitat management and pesticide release in combination, J. Appl. Ecol. 19 (1982) 337-348.
4. A. d'Onofrio, Pulse vaccination strategy in the SIR epidemic model: global asymptotic stable eradication in presence ofvaccine failures, Math. Comput. Modelling 36 (2002) 473-489.
5. A. d'Onofrio, Stability properties of pulse vaccination strategy in SEIR epidemic model, Math. Biosci. 179 (2002) 57-72.
6. H.J. Freedman, Graphical stability, enrichment, and pest control by a natural enemy, Math. Biosci. 31 (1976) 207-225.
7. J. Grasman, O.A.Van Herwaarden, L. Hemerik, J.C. Van Lenteren, A two-component model ofhost-parasitoid interactions: determination of the size of inundative releases of parasitoids in biological pest control, Math. Biosci. 169 (2001) 207-216.
8. A. Lakmeche, O. Arino, Bifurcation ofnon trivial periodic solutions ofimpulsive differential equations arising chemotherapeutic treatment, Dynamics Continuous, Discrete Impulsive System 7 (2000) 265-287.
9. A. Lakmeche, O. Arino, Nonlinear mathematical model of pulsed therapy of heterogenous tumors, Nord. Anal. 2 (2001) 455-465.
10. V. Lakshmikantham, D. Bainov, P. Simeonov, Theory ofImpulsive Differential Equations, World Scientific, Singapore, 1989.
11. J.C. Paneyya, A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competition environment, Bull. Math. Biol. 58 (1996) 425-447.
12. ED. Parker, Management of pest populations by manipulating densities ofboth host and parasites through periodic releases, in: C.B. Huffaker (Ed.), Biological Control, Plenum Press, NewYork, 1971.
13. M.G. Roberts, R.R. Kao, The dynamics ofan infectious disease in apopulation withbirthpulse, Math. Biosci. 149(1998)23-36.
14. B. Shulgin, L. Stone, Z. Agur, Pulse vaccination strategy in the SIR epidemic model, Bull. Math. Biol. 60 (1998) 1-26.
15. B. Shulgin, L. Stone, Z. Agur, Theoretical examination ofpulse vaccination policy in the SIR epidemic model, Math. Comput. Modelling 31 (4/5) (2000) 207-215.
16. S.Y. Tang, L.S. Chen, Density-dependent birth rate, birth pulses and their population dynamic consequences, J. Math. Biol. 44 (2002) 185-199.
17. University of California, Division of Agriculture and Natural Resources, Integrated Pest Management for Alfafa hay, Publication 3312, Publications, Division of Agriculture and Nature Resources, University of California, 6701 San Pablo Avenue, Oakland, CA 94608-1239, 1981.
18. University of California Statewide Integrated Pest Management Project, Division ofAgriculture and Natural Resources, Integrated Pest Management for Walnuts, 2nd ed., M.L. Flint (Ed.), University of California, Oakland, CA, Publication 3270, 1987.
19. J.C. Van Lenteren, Measures of success in biological control of anthropoids by augmentation of natural enemies, in: S. Wratten, G. Gurr (Eds.), Measures of Success in Biological Control, Kluwer Academic Publishers, Dordrecht, 2000.
20. J.C. Van Lenteren, Integrated pest management in protected crops, in: D. Dent (Ed.), Integrated Pest Management, Chapman & Hall, London, 1995.