Effects of habitat fragmentation and ecological invasion on population sizes

Computers and Mathematics with Applications

Volumn 38, Issue 1, 1999, Pages 1-11

  Cui, Jingan ^a,b   Chen, Lansun ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b XINJIANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BIOLOGY; CONSERVATION; DIFFERENTIAL EQUATIONS; ECOLOGY; SET THEORY; THEOREM PROVING;

ECOLOGICAL INVASION; HABITAT FRAGMENTATION; LOTKA-VOLTERRA DIFFUSION MODEL; NONAUTONOMOUS DIFFUSIVE LOGISTIC MODEL; PERMANENCE;

MATHEMATICAL MODELS;

EID: 0033164522     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(99)00162-5     Document Type: Article

References (20)

1. 1. J. Diamond, Overview of recent extinctions, In Conservation for the Twenty-First Century, (Edited by D. Western et al.), pp. 37-41, Oxford University Press, New York, (1989).
2. 2. D.A. Saunders, R.J. Hobbs and C.R. Margules, Biological consequences of ecosystem fragmentation: A review, Conservation Biology 5 (1), 18-32, (1991).
3. 3. J.D, Skellem, Random dispersal in theoretical population, Biometrika 38, 196-216, (1951).
4. 4. E. Beretta and Y. Takeuchi, Global asymptotic stability of Lotka-Volterra diffusion models with continuous time delay, SIAM J. Appl. Math. 48, 627-651, (1988).
5. 5. H.I. Freedman, B. Rai and P. Waltman, Mathematical models of population interactions with dispersal II: Differential survival in a change of habitat, J. Math. Anal. Appl. 115, 140-154, (1986).
6. 6. H.I. Preedman and P. Waltman, Mathematical models of population interactions with dispersal I: Stability of two habitats with and without a predator, SIAM J. Appl. Math. 32, 631-648, (1977).
7. 7. 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, 247-266, (1989).
8. 8. H.I. Freedman and Y. Takeuchi, Global stability and predator dynamics in a model of prey dispersal in a patchy environment, Nonlin. Anal T.M.A. 13, 993-1002, (1989).
9. 9. R. Mahbuba and L. Chen, On the nonautonomous Lotka-volterra competition system with diffusion, Diff. Equ. Dynamic. Syst. 2, 243-253, (1994).
10. 10. W. Wang, L. Chen and Z. Lu, Global stability of a population dispersal in a two-patch environment, Dynamic Systems and Applications 6, 207-216, (1997).
11. 11. J. Zhang and L. Chen, Periodic solutions of single-species nonautonomous diffusion models with continuous time delays, Mathl. Comput. Modelling 23 (7), 17-27, (1996).
12. 12. J. Zhang and L. Chen, Permanence and global stability for a two-species cooperative system with time delays in a two-patch environment, Computers Math. Applic. 32 (12), 101-108, (1996).
13. 13. F. Cao and L. Chen, Asymptotic behavior of nonautonomous diffusive Lotka-Volterra model, Syst. Sci. & Math. Sci. 11, 107-111, (1998).
14. 14. G. Zeng, L. Chen and J. Chen, Persistence and periodic orbits for two-species nonautonomous diffusion Lotka-Volterra models, Mathl. Comput. Modelling 20 (12), 69-80, (1994).
15. 15. C. Yucun, The urgent problems in reproduction of giant pandas, Chinese Wildlife (3), 3-5, (1994).
16. 16. Y. Zhou, Analysis on decline of wild alligator sinensis population, Sichuan Journal of Zoology 16 (3), 137-139, (1997).
17. 17. S. Wang, Y. Qu, Z. Jing, C. Jiang and Q. Wu, Research on the suitable living environment of the rana temporaria chensinensis larva, Chinese Journal of Zoology 32 (1), 38-41, (1997).
18. 18. J. Cui and L. Chen, The effect of diffusion on the time varying logistic population growth, Computers Math. Applic. 36 (3), 1-9, (1998).
19. 19. A. Tineo, An iterative scheme for the N-competing species problem, J. Diff. Equ. 116, 1-15, (1995).
20. 20. H.L. Smith, Cooperative systems of differential equation with concave nonlinearities, Nonlin. Anal. T.M.A. 10, 1037-1052, (1986).