Permanence for a delayed discrete three-level food-chain model with Beddington-DeAngelis functional response

Applied Mathematics and Computation

Volumn 187, Issue 2, 2007, Pages 1109-1119

  Xu, Changyong ^a   Wang, Meijuan ^a  

^a UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY   (China)

Author keywords

Beddington DeAngelis functional response; Food chain model; Permance

Indexed keywords

COMPUTATION THEORY; FUNCTION EVALUATION; FUNCTIONS; MATHEMATICAL MODELS;

BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE; FOOD-CHAIN MODEL; PERMANEANCE;

SUPPLY CHAINS;

EID: 34247209554     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.09.104     Document Type: Article

References (17)

1. Hsu S.B., Hwang T.W., and Kuang Y. A ratio-dependent food chain model and its applications to biological control. Math. Biosci. 181 (2003) 55-83
2. Beddington J.R. Mutual interference between parasites or predators and its effects on searching efficiency. J. Animal Ecol. 44 (1975) 331-340
3. DeAngelis D.L., Goldstein R.A., and ONeill R.V. A model for trophic interaction. Ecology 56 (1975) 881-892
4. Raid Kamel Naji, Alla Tariq Balasim, Dynamic behavior of a three food chain model with Beddington-DeAngelis functional response, Chaos Solutions & Fractals, in press.
5. Huo H.-F., and Li W.-t. Existence and global stability of a periodic food chain model with delays. Appl. Math. Comput. 162 (2005) 1333-1349
6. Sun Y.G., and Saker S.H. Positive periodic solutions of discrete three-level food-chain model of Holling type. Appl. Math. Comput. 180 (2006) 353-365
7. Xu R., and Chen L. Periodic solutions of a discrete time Lotka-Volterra type food-chain model with delays. Appl. Math. Comput. 171 (2005) 91-103
8. Zhang H., and Chen F. Positive periodic solutions for three-species food chain system with Beddington-DeAngelis functional response. J. FuZhou Univ. 32 (2004) 413-416 (in Chinese)
9. Fan Y.-H., and Li W.-t. Permanence for a delayed discrete ratio-dependent predator-prey system with Holling type functional response. J. Math. Anal. Appl. 299 (2004) 357-374
10. Wang L., and Wang M.Q. Ordinary Difference Equations (1989), Xinjiang University Press, Xinjiang (in Chinese)
11. Kocic V.L., and Ladas G. Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (1993), Kluwer Academic, London
12. Hwang T.W. Global analysis of the predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 290 (2004) 113-122
13. Hwang T.W. Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 281 (2003) 395-401
14. 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
15. Cantrell R.S., and Cosner C. Effect of domain size on the persistence of population in a diffusive food chain model with DeAngelis-Beddington functional response. Natural Resour. Model. 14 (2001) 335-367
16. 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
17. Dai B., Zhang N., and Zou J. Permance for the Michaelis-Menten type discrete three-species ratio-dependent food chain model with delay. J. Math. Anal. Appl. 324 (2006) 728-738