Extinction and permanence of a two-prey one-predator system with impulsive effect

Mathematical Medicine and Biology

Volumn 20, Issue 4, 2003, Pages 309-325

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

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b ANSHAN NORMAL UNIVERSITY   (China)

^c CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Extinction; Impulsive effect; Permanence; Two prey one predator system

Indexed keywords

PREDATOR PREY SYSTEMS;

CRITICAL VALUE; EXTINCTION; FLOQUET THEOREM; GLOBALLY ASYMPTOTICALLY STABLE; IMPULSIVE EFFECTS; PERMANENCE; PERTURBATION SKILLS; POSITIVE PERIODIC SOLUTION; SMALL AMPLITUDE PERTURBATIONS; TWO-PREY ONE-PREDATOR SYSTEM;

PROBLEM SOLVING;

ARTICLE; COMPETITIVE INHIBITION; MATHEMATICAL MODEL; MATHEMATICAL PHENOMENA; MICROBIAL POPULATION DYNAMICS; PEST CONTROL; PREDATOR PREY INTERACTION; SIMULATION; SPECIES COEXISTENCE; SPECIES CONSERVATION; SPECIES EXTINCTION;

INSECTA;

EID: 0842325113     PISSN: 14778599     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb/20.4.309     Document Type: Article

References (21)

1. DeBach, P. and Rosen, D. (1991) Biological Control by Natural Enemies 2nd edn. Cambridge: Cambridge University Press.
2. Bainov, D. D & Simenov, P. S. (1993) Impulsive Differential Equations: Periodic Solutions and Applications. New York: Wiley.
3. Ballinger, G. & Liu, X. (1997) Permanence of population growth models with impulsive effects. Math. Comput. Modelling, 26, 59-72.
4. Cherry, A. J., Lomer, C. J., Djegui, D. & Schulthess, F. (1999a) Pathogen incidence and their potential as microbial control agents in IPM of maize stemborers in West Africa. Biocontrol, 44, 301-327.
5. Cramer, N. F. & May, R. M. (1972) Interspecific competition, predation and species diversity: A comment. J. Theor. Biol., 34, 289-293.
6. Ferron, P. (1981) Pest control using the fungi Beauveria and Metarhizinm. Microbial Control in Pests and Plant Diseases. (H. D. Burges, ed.). London: Academic.
7. Freedman, H. J. (1976) Graphical stability, enrichment, and pest control by a natural enemy. Math. Biosci., 31, 207-225.
8. Fujii, K. (1977) Complexity-stability relationship of two-prey-one-predator species system model: Local and global stability. J. Theor. Biol., 69, 613-623.
9. Grasman, J., Van Herwaarden, O. A., Hemerik, L. et al. (2001) A two-component model of host-parasitoid interactions: Determination of the size of inundative releases of parasitoids in biological pest control. 169, 207-216.
10. Hsu, S. B. (1981) Predator-mediated coexistence and extinction. Math. Biosci., 54, 231-248.
11. Lakmeche, A. & Arino, O. (2000) Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment. Dynam. Contin. Discr. Impuls. Sys., 7, 165-287.
12. Lakshmikantham, V., Bainov, D. D. & Simeonov, P. S. (1989) Theory of Impulsive Differential Equations. Singapore: World Scientific.
13. Van Lenteren, J. C. (2000) Measures of success in biological control of anthropoids by augmentation of natural enemies. Measures of Success in Biological Control. (S. Wratten & G. Gurr, eds). Dordrdcht: Kluwer.
14. Luff, M. L. (1983) The potential of predators for pest control. Agri. Ecos. Environ., 10, 159-181.
15. D'Onofrio, A. (2002) Stability properties of pulse vaccination strategy in SEIR epidemic model. Math. Biosci., 179, 57-72.
16. Panetta J. C. (1996) A mathematical model of periodically pulsed chemotherapy: Tumor recurrence and metastasis in a competitive environment. Bull. Math. Biol., 58, 425-447.
17. Parrish, J. D. & Saila, S. B. (1970) Interspecific competition, predation and species diversity. J. Theor. Biol., 27, 207-220.
18. Roberts, M. G. & Kao, R. R. (1998) The dynamics of an infectious disease in a population with birth pulses. Math. Biosci., 149, 23-36.
19. Shulgin, B., Stone, L. & Agur, Z. (1998) Pulse vaccination strategy in the SIR epidemic model. Bull. Math. Biol., 60, 1-26.
20. Tang, S. Y. & Chen, L. S (2002) Density-dependent birth rate, birth pulses and their population dynamic consequences. J. Math. Biol., 44, 185-199.
21. Takeuchi, Y. & Adachi, N. (1983) Existence and bifurcation of stable equilibrium in two-prey one-predator communities. Bull. Math. Biol., 45, 877-900.