Permanence and global stability for nonlinear discrete model

Advances in Complex Systems

Volumn 9, Issue 1-2, 2006, Pages 31-40

  Xiaoxing, Chen ^a  

^a FUZHOU UNIVERSITY   (China)

Author keywords

Discrete; Global stability; Nonlinear; Permanence

Indexed keywords

EID: 33747055584     PISSN: 02195259     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219525906000628     Document Type: Article

References (33)

1. Gopalsamy, K., Global asymptotic stability in a periodic Lotka-Volterra system, J. Austral. Math. Soc. Ser. B 27, 66-72 (1985).
2. Zhao, X. Q., The qualitative analysis of n-species Lotka-Volterra periodic competition systems, Math. Comput. Modell. 15(11), 3-8 (1991).
3. Tineo, A. and Alvarz, C., A different consideration about the globally asymptotically stable solution of the periodic n-competing species problem, J. Math. Anal. Appl. 159, 44-55 (1991).
4. Gopalsamy, K., Exchange of equilibria in two Lotka-Volterra competition models, J. Aust. Math. Soc. Ser. B 24, 160-170 (1982).
5. Li, Y. K., Periodic solutions for delay Lotka-Volterra competition systems, J. Math. Anal. Appl. 246, 230-244 (2000).
6. Peng, Q. L. and Chen, L. S., Asymptotic behavior of the nonautonomous two-species Lotka-Volterra competition models, Comput. Math. Applic. 27(12), 53-60 (1994).
7. Ahmad, S., On the nonautonomous Lotka-Volterra competition models, Proc. Amer. Math. Soc 117(1), 199-205 (1993).
8. Montes de Oca, F. and Zeeman, M. L., Extinction in nonautonomous competition Lotka-Volterra systems, Proc. Amer. Math. Soc. 124, 3677-3687 (1996).
9. Tineo, A., An iterative scheme for the N-competing species problem, J. Differ. Equations 116, 1-15 (1995).
10. Tineo, A., On the asymptotic behavior of some population model, J. Math. Anal. Appl. 167, 516-529 (1992).
11. Ahmad, S., On almost periodic solutions of the competing species problems, Proc. Amer. Math. Soc. 102, 855-861 (1988).
12. Ahmad, S. and Lazer, A. C., Necessary and sufficient average growth in a Lotka-Volterra system, Nonlin. Anal. 34, 191-228 (1998).
13. Gui, Z. J. and Chen, L. S., Asymptotic behavior of the nonautonomous Lotka-Volterra competition equations, Acta. Math. Sci. 22A(4), 465-470 (2002).
14. Chattopadhyay, J., Effect of toxic substance on a two-species competitive system, Ecol. Model 84, 287-289 (1996).
15. Maynard-Smith, J., Models in Ecology (Cambridge University Press, Cambridge, 1974).
16. Fan, M. and Wang, K., Global periodic solutions of a generalized n-species Gilpin-Ayala competition model, Comput. Math. Appl. 40, 1141-1151 (2000).
17. Chen, X. X. and Chen, F. D., Almost periodic solutions of a population equation with feedback control, Nonlinear Real World Appl. Ser. B, in press.
18. Chen, F. D., Persistence and global stability for nonautonomous cooperative system with diffusion and time delay, Acta Sci. Natur. Univers. Pekinensis 39(1), 22-28 (2003).
19. Chen, F. D., Sun, D. X. and Shi, J. L., Periodicity in a food-limited population model with toxicants and state dependent delays, J. Math. Anal. Appl. 288(1), 132-142 (2003).
20. Chen, F. D., Periodicity in a nonlinear predator-prey system with state dependent delays, Acta Math. Appl. Sinica, Engl. Ser. 21(1), 49-60 (2005).
21. Chen, F. D., On a nonlinear non-autonomous predator-prey model with diffusion and distributed delay, J. Comput. Appl. Math. 80(1), 33-49 (2005).
22. Chen, F. D. and Lin, S. J., Periodicity in a logistic type system with several delays, Comput. Math. Appl. 48(1-2), 35-44 (2004).
23. Chen, F. D., On a periodic multi-species ecological model, Appl. Math. Comput. in press.
24. Freedman, H. I., Deterministic Mathematical Models in Population Ecology (Marcel Dekker, New York, 1980).
25. Agarwal, R. P., Difference Equations and Inequalities: Theory, Methods and Applications, Monographs and Textbooks in Pure and Applied Mathematics, No. 228 (Marcel Dekker, New York, 2000).
26. Goh, B. S., Management and Analysis of Biological Populations (Elsevier Scientific, The Netherlands, 1980).
27. Murry, J. D., Mathematical Biology (Springer-Verlag, New York, 1989).
28. Fan, M. and Agarwal, S., Periodic solutions of nonautonomous discrete predator-prey system of Lotka-Volterra type, Appl. Anal. 81(4), 801-812 (2002).
29. Fan, M. and Agarwal, S., Periodic solutions for a class of discrete time competition systems, Nonlin. Studies 9(3), 249-261 (2002).
30. Fan, M. and Wang, K., Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system, Math. Comput. Modell. 35(9-10), 951-961 (2002).
31. Huo, H. F. and Li, W. T., Permanence and global stability for nonautonomous discrete model of plankton allelopathy, Appl. Math. Lett. 17, 1007-1013 (2004).
32. Agarwal, R. P., Difference Equations and Inequalities, Theory, Method and Applications Monographs and Textbooks in Pure and Applied Mathematics, No. 228 (Marcel Dekker, New York, 2000).
33. Wang, W. D. and Lu, Z. Y., Global stability of discrete models of Lotka-Volterra type, Nonlin. Anal. Theor: Meth. Appl. 35, 1019-1030 (1999).