AN impulsive predator-prey system with Beddington-DeAngelis functional response and time delay

International Journal of Biomathematics

Volumn 1, Issue 1, 2008, Pages 1-17

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

^a JIANGSU UNIVERSITY   (China)

^b GHEORGHE ASACHI TECHNICAL UNIVERSITY OF IASI   (Romania)

^c CENTRAL EUROPEAN UNIVERSITY   (Hungary)

^d DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Beddington DeAngelis functional response; impulsive perturbation; maturation delay; Predator prey system; stage structure

Indexed keywords

EID: 84863116818     PISSN: 17935245     EISSN: 17937159     Source Type: Journal    
DOI: 10.1142/S1793524508000072     Document Type: Article

References (23)

1. P. Yodzis, Predator-prey theory and management of multispecies fisheries, Ecol. Appl. 4 (1994) 51-58.
2. R. Arditi and L. R. Ginzburg, Coupling in predator-prey dynamics: Ratiodependence, J. Theor. Biol. 139 (1989) 311-326.
3. C. Huisman and R. J. DeBoer, A formal derivation of the Beddington functional response, J. Theor. Biol. 185 (1997) 389-400.
4. A. Abrams and L. R. Ginzburg, The nature of predation: Prey dependent, ratio dependent or neither? Trends Ecol. Evol. 15 (2000) 337-341.
5. Y. Kuang and E. Beretta, Global qualitative analysis of a ratio-dependent predatorprey system, J. Math. Biol. 36 (1998) 389-406.
6. A. P. Gutierrez, The physiological basis of ratio-dependent predator-prey theory: A metabolic pool model of Nicholsons blowflies as an example, Ecology 73 (1992) 1552-1563.
7. C. Jost and S. Ellner, Testing for predator dependence in predator-prey dynamics: A nonparametric approach, Proc. Royal Soc. London Ser. B 267 (2000) 1611-1620.
8. G. T. Skalski and J. F. Gilliam, Functional responses with predator interference: Viable alternatives to the Holling type II model, Ecology 82 (2001) 3083-3092.
9. J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, J. Anim. Ecol. 44 (1975) 331-340.
10. D. L. DeAngelis, R. A. Goldstein and R. V. O'Neill, A model for tropic interaction, Ecology 56 (1975) 881-892.
11. Z. W. Hwang, Global analysis of the predator-prey system with Beddington- DeAngelis functional response, J. Math. Anal. Appl. 281 (2003) 395-401.
12. Z. W. Hwang, Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response, J. Math. Anal. Appl. 290 (2004) 113-122.
13. Z. Liu and R. Yuan, Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response, J. Math. Anal. Appl. 296 (2004) 521-537.
14. E. Beretta and Y. Kuang, Global analysis in some delayed ratio-dependent predatorprey systems, Nonlinear Anal. TMA 32 (1998) 381-408.
15. S. Liu and E. Beretta, A stage-structured predator-prey model of Beddington- DeAngelis type, SIAM J. Appl. Math. 66 (2006) 1101-1129.
16. K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics (Kluwer Academic Publishers, Boston, 1991).
17. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics (Springer, New York, 1993).
18. M. Fan and Y. Kuang, Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response, J. Math. Anal. Appl. 295 (2004) 15-39.
19. V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations (World Scientific, Singapore, 1989).
20. D. D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications (Longman, London, 1993).
21. R. E. Gaines and R. M. Mawhin, Coincidence Degree and Nonlinear Differential Equations (Springer-Verlag, Berlin, 1977).
22. A. Halanay, Differential Equations: Stability, Oscillations, Time Lags (Academic Press, New York, 1966).
23. S. Liu, L. Chen, G. Luo and Y. Jiang, Asymptotic behavior of competitive Lotka- Volterra system with stage structure, J. Math. Anal. Appl. 271 (2002) 124-138.