Dispersal permanence of a periodic predator-prey system with Beddington-DeAngelis functional response

Nonlinear Analysis, Theory, Methods and Applications

Volumn 64, Issue 3, 2006, Pages 440-456

  Cui, Jing'an ^a  

^a NANJING NORMAL UNIVERSITY   (China)

Author keywords

Beddington DeAngelis functional response; Dispersal; Permanence; Predator prey system

Indexed keywords

NUMERICAL METHODS;

BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE; DISPERSAL; PERMANENCE; PREDATOR-PREY SYSTEM;

NONLINEAR SYSTEMS;

EID: 28844486610     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.06.022     Document Type: Article

References (20)

1. L.J.S. Allen Persistence and extinction in Lotka-Volterra reaction-diffusion equations Math. Biosci. 65 1983 1 12
2. E. Beretta, and F. Solimano Global stability and periodic orbits for two patch predator-prey diffusion delay models Math. Biosci. 85 1987 153 183
3. E. Beretta, and Y. Takeuchi Global asymptotic stability of Lotka-Volterra diffusion models with continuous time delays SIAM J. Appl. Math. 48 1988 627 651
4. J. Cui, and L. Chen The effect of diffusion on the time varying Logistic population growth Comput. Math. Appl. 36 1998 1 9
5. J. Cui, and L. Chen Permanent and extinction in logistic and Lotka-Volterra systems with diffusion J. Math. Anal. Appl. 258 2001 512 535
6. J. Cui, Y. Takeuchi, and Z. Lin Permanence and extinction for dispersal population systems J. Math. Anal. Appl. 298 2004 73 97
7. H.I. Freedman, and P. Moson Persistence definitions and their connections Proc. AMS 109 1990 1025 1032
8. H.I. Freedman, and Y. Takeuchi Predator survival versus extinction as a function of dispersal in a predator-prey model with patchy environment Appl. Anal. 31 1989 247 266
9. H.I. Freedman, and Y. Takeuchi Global stability and predator dynamics in a model of prey dispersal in a patchy environment Nonlinear Anal. TMA 13 1989 993 1002
10. H.I. Freedman, and P. Waltman Mathematical models of population interaction with dispersal. I. Stability of two habitats with and without a predator SIAM J. Math. 32 1977 631 648
11. Y. Kuang, and Y. Takeuchi Predator-prey dynamics in models of prey dispersal in two-patch environments Math. Biosci. 120 1994 77 98
12. M. Luo, and Z. Ma The persistence of two species Lotka-Volterra model with diffusion J. Biomath. 12 1997 52 59 (in Chinese)
13. H.L. Smith Cooperative systems of differential equation with concave nonlinearities Nonlinear Anal. 10 1986 1037 1052
14. Y. Takeuchi Global Dynamical Properties of Lotka-Volterra Systems 1996 World Scientific Singapore
15. Z. Teng, and L. Chen Permanence and extinction of periodic predator-prey systems in patchy environment with delay Nonlinear Anal.: Real World Appl. 4 2003 335 364
16. H.R. Thieme Uniform persistence and permanence for non-autonomous semiflows in population biology Math. Biosci. 166 2000 173 201
17. R. Xu, M.A.J. Chaplain, and F.A. Davidson Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments Nonlinear Anal.: Real World Appl. 5 2004 183 206
18. T. Yoshizawa, Stability by Liapnov's Second Method, publication no. 9, Mathematical Society of Japan, Tokyo, 1966.
19. X.-Q. Zhao The qualitative analysis of N-species Lotka-Volterra periodic competition systems Math. Comp. Modeling 15 1991 3 8
20. H. Zhu, S.A. Campbell, and G. Wolkowicz Bifurcation analysis of a predator-prey system with nonmonotonic functional response SIAM J. Appl. Math. 63 2002 636 682