Permanence, extinction and periodic solution of predator-prey system with Beddington-DeAngelis functional response

Journal of Mathematical Analysis and Applications

Volumn 317, Issue 2, 2006, Pages 464-474

  Cui, Jing'an ^a   Takeuchi, Yasuhiro ^b  

^a NANJING NORMAL UNIVERSITY   (China)

^b SHIZUOKA UNIVERSITY   (Japan)

Author keywords

Beddington DeAngelis functional response; Extinction; Periodic solution; Permanence; Predator prey

Indexed keywords

EID: 33644590203     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.10.011     Document Type: Article

References (26)

1. A. Abrams L.R. Ginzburg The nature of predation: Prey dependent, ratio dependent or neither? Trends in Ecology and Evolution 15 2000 337-341
2. S. Ahmad A.C. Lazer Average conditions for global asymptotic stability in a nonautonomous Lotka-Volterra system Nonlinear Anal. 40 2000 37-49
3. J.R. Beddington Mutual interference between parasites or predators and its effect on searching efficiency J. Animal Ecol. 44 1975 331-340
4. T.A. Burton V. Hutson Permanence for nonautonomous predator-prey systems Differential Integral Equations 4 1991 1269-1280
5. G.J. Butler H.I. Freedman Periodic solution of a predator-prey system with periodic coefficients Math. Biosci. 55 1981 27-38
6. R.S. Cantrell C. Cosner On the dynamics of predator-prey models with the Benddington-DeAngelis functional response J. Math. Anal. Appl. 257 2001 206-222
7. C. Cosner D.L. DeAngelis J.S. Ault D.B. Olson Effects of spatial grouping on the functional response of predators Theor. Pop. Biol. 56 1999 65-75
8. J. Cui, Permanence of predator-prey system with periodic coefficients, Math. Comput. Modelling, in press
9. J. Cui L. Chen Permanence and extinction in Logistic and Lotka-Volterra systems with diffusion J. Math. Anal. Appl. 258 2001 512-535
10. J.M. Cushing Periodic solutions of two species interaction models with lags Math. Biosci. 31 1976 143-146
11. J.M. Cushing Stable limit cycles of time-dependent multispecies interactions Math. Biosci. 31 1976 259-273
12. J.M. Cushing Periodic time-dependent predator-prey systems SIAM J. Appl. Math. 32 1977 82-95
13. D.L. DeAngelis R.A. Goldstein R.V. O'Neill A model for trophic interaction Ecology 56 1975 881-892
14. T. Ding H. Huang F. Zanolin A priori bounds and periodic solution for a class of planar systems with applications to Lotka-Volterra equations Discrete Contin. Dyn. Syst. 1 1995 103-117
15. M. Fan Y. Kuang Dynamics of nonautonomous predator-prey system with the Beddington-DeAngelis functional response J. Math. Anal. Appl. 295 2004 15-39
16. H.I. Freedman P. Moson Persistence definitions and their connections Proc. Amer. Math. Soc. 109 1990 1025-1032
17. T. Hwang Global analysis of the predator-prey system with Beddington-DeAngelis functional response J. Math. Anal. Appl. 281 2003 395-401
18. J. Lopez-Gomez R. Ortega A. Tineo The periodic predator-prey Lotka-Volterra model Adv. Differential Equations 1 1996 403-432
19. Z. Teng Uniform persistence of the periodic predator-prey Lotka-Volterra systems Appl. Anal. 72 1998 339-352
20. Z. Teng L. Chen The positive periodic solutions of periodic Kolmogorov-type systems with delays Acta Math. Appl. Sinica 22 1999 446-456
21. H.R. Thieme Uniform persistence and permanence for nonautonomous semiflows in population biology Math. Biosci. 166 2000 173-201
22. A. Tineo An iterative scheme for the N competing species problem J. Differential Equations 116 1995 1-15
23. A. Tineo Permanence of a large class of periodic predator-prey systems J. Math. Anal. Appl. 241 2000 83-91
24. K. Wang Persistence for nonautonomous predator-prey systems with infinite delay Acta Math. Sinica 40 1997 321-332
25. X.-Q. Zhao The qualitative analysis of N-species Lotka-Volterra periodic competition systems Math. Comput. Modelling 15 1991 3-8
26. X.-Q. Zhao Dynamical Systems in Population Biology 2003 Springer-Verlag New York