Permanence of delayed population model with dispersal loss

Mathematical Biosciences

Volumn 201, Issue 1-2, 2006, Pages 143-156

  Takeuchi, Yasuhiro ^a   Cui, Jing'an ^b   Miyazaki, Rinko ^a   Saito, Yasuhisa ^a  

^a SHIZUOKA UNIVERSITY   (Japan)

^b NANJING NORMAL UNIVERSITY   (China)

Author keywords

Dispersal time delay; Liapunov Razumikhin theorem; Periodic solution; Permanence

Indexed keywords

DIFFERENTIAL EQUATIONS; DISPERSIONS;

DISPERSAL TIME DELAY; LIAPUNOV-RAZUMIKHIN THEOREM; PERIODIC SOLUTION; PERMANENCE;

MATHEMATICAL MODELS;

DISPERSAL; POPULATION MODELING;

ARTICLE; BIOLOGICAL TRAIT; DISPERSION; FOOD ANALYSIS; MATHEMATICAL COMPUTING; PATCH TEST; POPULATION MODEL; SPECIES; SPECIES DIFFERENTIATION; SPECIES EXTINCTION; SYSTEM ANALYSIS;

ANIMAL MIGRATION; ANIMALS; ECOSYSTEM; MODELS, BIOLOGICAL; POPULATION DYNAMICS;

EID: 33646827009     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2005.12.012     Document Type: Article

References (31)

1. Allen L.J.S. Persistence and extinction in single-species reaction-diffusion models. Bull. Math. Biol. 45 (1983) 209
2. Allen L.J.S. Persistence, extinction and critical patch number for island populations. J. Math. Biol. 24 (1987) 617
3. Beretta E., and Takeuchi Y. Global stability of single-species diffusion Volterra models with continuous time delays. Bull. Math. Biol. 49 (1987) 431
4. Beretta E., and Takeuchi Y. Global asymptotic stability of Lotka-Volterra diffusion models with continuous time delays. SIAM J. Appl. Math. 48 (1988) 627
5. Beretta E., Solimano F., and Takeuchi Y. Global stability and periodic orbits for two patch predator-prey diffusion delay models. Math. Biosci. 85 (1987) 153
6. Cui J., and Chen L. The effect of diffusion on the time varying logistic population growth. Computers Math. Appl. 36 (1998) 1
7. Cui J., and Chen L. Permanent and extinction in logistic and Lotka-Volterra systems with diffusion. J. Math. Anal. Appl. 258 (2001) 512
8. Cui J., Takeuchi Y., and Lin Z. Permanent and extinction for dispersal population systems. J. Math. Anal. Appl. 298 (2004) 73
9. Freedman H.I. Deterministic Mathematical Models in Population Ecology (1980), Marcel Dekker, New York
10. Freedman H.I., and Waltman P. Mathematical models of population interaction with dispersal. I. Stability of two habitats with and without a predator. SIAM J. Math. 32 (1977) 631
11. Freedman H.I. Single species migration in two habitats: persistence and extinction. Math. Model. 8 (1987) 778
12. Freedman H.I., and Takeuchi Y. Global stability and predator dynamics in a model of prey dispersal in a patchy environment. Nonlinear Anal. TMA 13 (1989) 993
13. Hastings A. Spatial heterogeneity and the stability of predator prey systems. Theoret. Populat. Biol. 12 (1977) 37
14. Kuang Y., and Takeuchi Y. Predator-prey dynamics in models of prey dispersal in two-patch environments. Math. Biosci. 120 (1994) 77
15. Levin S. Dispersion and population interactions. Am. Nat. 108 (1974) 207
16. Lu Z., and Takeuchi Y. Global asymptotic behavior in single-species discrete diffusion systems. J. Math. Biol. 32 (1993) 67
17. Takeuchi Y. Global Dynamical Properties of Lotka-Volterra Systems (1996), World Scientific, Singapore
18. Takeuchi Y. Global stability in generalized Lotka-Volterra diffusion systems. J. Math. Anal. Appl. 116 (1986) 209
19. Takeuchi Y. Diffusion effect on stability of Lotka-Volterra model. Bull. Math. Biol. 46 (1986) 585
20. Takeuchi Y. Cooperative system theory and global stability of diffusion models. Acta Appl. Math. 14 (1989) 49
21. Takeuchi Y. Diffusion-mediated persistence in two-species competition Lotka-Volterra model. Math. Biosci. 95 (1989) 65
22. Takeuchi Y. Conflict between the need to forage and the need to avoid competition: persistence of two-species model. Math. Biosci. 99 (1990) 181
23. Y. Takeuchi, J. Cui, R. Miyazaki, Y. Saito, Permanence and periodic solutions of dispersal population model with time delays, preprint.
24. Teng Z., and Lu Z. The effect of dispersal on single-species nonautonomous dispersal models with delays. J. Math. Biol. 42 (2001) 439
25. Vance R.R. The effect of dispersal on population stability in one-species, discrete space population growth models. Am. Nat. 123 (1984) 230
26. Wang W., and Chen L. Global stability of a population dispersal in a two-patch environment. Dyn. Syst. Appl. 6 (1997) 207
27. Smith H.L. Monotone Dynamical Systems, an Introduction to the Theory of Competitive and Cooperative Systems (1995), AMS, Providence, RI
28. Tineo A. An iterative scheme for the N-competing species problem. J. Diff. Equat. 116 (1995) 1
29. Zhao X.Q. The qualitative analysis of N-species Lotka-Volterra periodic competition systems. Math. Comp. Model. 15 (1991) 3
30. Teng Z., and Chen L. The positive periodic solutions of periodic Kolmogorov type systems with delays. Acta Math. Appl. Sinica 22 (1999) 446
31. Kuang Y. Delay Differential Equations with Applications in Population Dynamics (1993), Academic Press, San Diego, CA