Permanence and global stability for a two-species cooperative system with time delays in a two-patch environment

Computers and Mathematics with Applications

Volumn 32, Issue 12, 1996, Pages 101-108

  Zhang, Jingru ^a   Chen, Lansun ^b  

^a XINJIANG UNIVERSITY   (China)

^b INSTITUTE OF APPLIED MATHEMATICS   (China)

Author keywords

Dispersal; Global asymptotic stability; Permanence; Time delay

Indexed keywords

ECOLOGY; ECOSYSTEMS; MATHEMATICAL MODELS; POPULATION STATISTICS;

GLOBAL STABILITY; PERMANENCE; TIME DELAYS; TWO PATCH ENVIRONMENT; TWO SPECIES COOPERATIVE SYSTEM;

ASYMPTOTIC STABILITY;

EID: 0030413307     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(96)00210-6     Document Type: Article

References (12)

1. Yang Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, CA, (1993).
2. J.D. Skellam, Random dispersal in theoretical population, Biometrika 38, 196-218 (1951).
3. F. Rothe, Convergence to the equilibrium state in the Volterra-Loyka diffusion equations, J. Math. Biol. 3, 319-324 (1976).
4. A. Leung, Limiting behavior for a prey-predator model with diffusion and crowding effects, J. Math. Biol. 6, 87-93 (1978).
5. Zhengyi Lu and Y. Takeuchi, Permanence and global stability for cooperative Lotka-Volterra diffusion systems, Nonli. Anal. 10, 963-975 (1992).
6. E. Berreta and Y. Takeuchi, Global asymptotic stability of Lotka-Volterra diffusion models with continuous time delays, SIAM J. Appl. Math. 48, 627-651 (1988).
7. H.I. Freedman, Single species migration in two habitats: Persistence and extinction, Mathl. Modelling. 8, 778-780 (1987).
8. H.I. Freedman and Y. Takeuchi, Predator survival versus extinction as a function of dispersal in a predator-prey model with patchy environment, Nonli. Anal. 13, 993-1002 (1989).
9. R.M. May, Theoretical Ecology, Principle and Applications, Sounders, Philadelphia, PA, (1976).
10. Lansun Chen, Models and Research Methods of Mathematical Ecology, Science Press, Beijing, (1988).
11. Jingan Cui, Global asymptotic stability in n-species cooperative system with time delays, Sys. Sci. and Math. Sci. 7, 45-48 (1994).
12. K. Gopalsamy, Stability and Oscillation in Delay Differential Equations of Population Dynamics, Kluwer Academic, (1992).