Coexistence and stability of predator-prey model with Beddington-DeAngelis functional response and stage structure

Journal of Mathematical Analysis and Applications

Volumn 342, Issue 1, 2008, Pages 446-460

  Liu, Shengqiang ^a   Zhang, Jianhua ^b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b XIAMEN UNIVERSITY   (China)

Author keywords

Beddington DeAngelis; Delay; Predator interference; Stage structure

Indexed keywords

EID: 39949085435     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.12.038     Document Type: Article

References (28)

1. Arditi R., and Ginzburg L.R. Coupling in predator-prey dynamics: Ratio-dependence. J. Theoret. Biol. 139 (1989) 311-326
2. Beddington J.R. Mutual interference between parasites or predators and its effect on searching efficiency. J. Animal Ecol. 44 (1975) 331-341
3. Cantrell R.S., and Cosner C. On the dynamics of predator-prey models with the Beddington-DeAngelis functional response. J. Math. Anal. Appl. 257 (2001) 206-222
4. Cantrell R.S., Cosner C., and Ruan S.G. Intraspecific interference and consumer-resource dynamics. Discrete Contin. Dyn. Syst. Ser. B 4 (2004) 527-546
5. Cosner C., DeAngelis D.L., and Ault J.S. Effects of spatial grouping on the functional response of predators. Theoret. Popul. Biol. 56 (1999) 65-75
6. Crowley P.H., and Martin E.K. Functional response and interference within and between year classes of a dragonfly population. J. N. Am. Benthol. Soc. 8 (1989) 211-221
7. DeAngelis D.L., Goldsten R.A., and Neill R. A model for trophic interaction. Ecology 56 (1975) 881-892
8. Fan M., and Kuang Y. Dynamics of a nonautonomous predator prey system with the Beddington-DeAngelis functional response. J. Math. Anal. Appl. 295 (2004) 15-39
9. Gourley S.A., and Kuang Y. A stage structured predator-prey model and its dependence on through-stage delay and death rate. J. Math. Biol. 49 (2004) 188-200
10. Hale J.K., and Waltman P. Persistence in infinite-dimensional systems. SIAM J. Math. Anal. 20 (1989) 388-395
11. Hassell M.P., and Varley C.C. New inductive population model for insect parasites and its bearing on biological control. Nature 223 (1969) 1133-1137
12. Holling C.S. The components of predation as revealed by a study of small mammal predation of the European pine sawfly. Canad. Entomologist 91 (1959) 293-320
13. Holling C.S. Some characteristics of simple types of predation and parasitism. Canad. Entomologist 91 (1959) 385-395
14. Hsu S.B., Hubbell S.P., and Waltman P. Competing predators. SIAM J. Appl. Math. 35 (1978) 617-625
15. Hwang Z.W. Global analysis of the predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 281 (2003) 395-401
16. Hwang Z.W. Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 290 (2004) 113-122
17. Kuang Y., and Beretta E. Global qualitative analysis of a ratio-dependent predator-prey system. J. Math. Biol. 36 (1998) 389-406
18. Liu S., and Beretta E. A stage-structured predator-prey model of Beddington-DeAngelis type. SIAM J. Appl. Math. 66 (2006) 1101-1129
19. Liu S., Chen L., Luo G., and Jiang Y. Asymptotic behavior of competitive Lotka-Volterra system with stage structure. J. Math. Anal. Appl. 271 (2002) 124-138
20. Liu S., Chen L., and Liu Z. Extinction and permanence in nonautonomous competitive stage structured system with stage structure. J. Math. Anal. Appl. 274 (2002) 667-684
21. Liu Z., and Yuan R. Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 296 (2004) 521-537
22. Qiu Z.P., Yu J., and Zou Y. The asymptotic behavior of a chemostat model with the Beddington-DeAngelis functional response. Math. Biosci. 187 (2004) 175-187
23. Ruxton G., Gurney W.S.C., and Deroos A. Interference and generation cycles. Theoret. Popul. Biol. 42 (1992) 235-253
24. Skalski G.T., and Gilliam J.F. Functional responses with predator interference: Viable alternatives to the Holling type II model. Ecology 82 (2001) 3038-3092
25. Thieme H.R. Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J. Math. Anal. 24 (1993) 407-435
26. Hwang Z.W. Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 290 (2004) 113-122
27. Hutson V., and Schmitt K. Permanence in dynamical systems. Math. Biosci. 111 (1992) 1-71
28. Murdoch W.W., Briggs C.J., and Nisbet R.M. Consumer-Resource Dynamics (2003), Princeton University Press, Princeton