Existence and global attractivity of positive periodic solutions for delay Lotka-Volterra competition patch systems with stocking

Journal of Mathematical Analysis and Applications

Volumn 293, Issue 1, 2004, Pages 190-209

  Fang, Hui ^a,b   Wang, Zhicheng ^a  

^a HUNAN UNIVERSITY   (China)

^b KUNMING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Coincidence degree; Global attractivity; Lotka Volterra competition patch system; Lyapunov functional; Positive periodic solution; Stocking rate

Indexed keywords

EID: 2342483169     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2003.12.036     Document Type: Article

References (27)

1. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993.
2. J.M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, in: Lecture Notes in Biomathematics, vol. 20, Springer-Verlag, New York, 1977.
3. K. Gopalsamy, Stability and Oscillation in Delay Differential Equations of Population Dynamics, in: Mathematics and Its Applications, vol. 74, Kluwer Academic, Dordrecht, 1992.
4. I. Gyori, G. Ladas, Oscillation Theory of Delay Differential Equations, Oxford Science, Oxford, 1991.
5. R.M. May, Stability and Complex in Model Ecosystem, Princeton Univ. Press, Princeton, NJ, 1974.
6. Z.Q. Zhang, Z.C. Wang, Periodic solutions for a two-species nonautonomous competition Lotka-Volterra system with time delay, J. Math. Anal. Appl. 265 (2002) 38-48.
7. H. Bereketoglu, I. Györi, Global asymptotic stability in a nonautonomous Lotka-Volterra type system with infinite delay, J. Math. Anal. Appl. 210 (1997) 279-291.
8. J.G. Zhang, L.S. Chen, X.D. Chen, Persistence and global stability for two-species nonautonomous competition Lotka-Volterra system with time delay, Nonlinear Anal. 37 (1999) 1019-1028.
9. M. Fan, K. Wang, D.Q. Jiang, Existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with several deviating arguments, Math. Biosci. 160 (1999) 47-61.
10. G.Z. Zeng, L.S. Chen, J.F. Chen, Persistence and periodic orbits for two-species nonautonomous diffusion Lotka-Volterra models, Math. Comput. Modelling 20 (1994) 69-80.
11. W. Wang, P. Fergola, C. Tenneriello, Global attractivity of periodic solutions of population models, J. Math. Anal. Appl. 211 (1997) 498-511.
12. Y.K. Li, Periodic solutions for delay Lotka-Volterra competition system, J. Math. Anal. Appl. 246 (2000) 230-244.
13. F. Brauer, A.C. Soudack, Coexistence of properties of some predator-prey systems under constant rate harvesting and stocking, J. Math. Biol. 12 (1981) 101-114.
14. F. Brauer, A.C. Soudack, On constant effort harvesting and stocking in a class of predator-prey systems, J. Theor. Biol. 95 (1982) 247-252.
15. L. Erbe, W. Krawcewicz, J. Wu, A composite coincidence degree with applications to boundary value problems of neutral equations, Trans. Amer. Math. Soc. 335 (1953) 459-478.
16. W. Krawcewicz, J. Wu, Theory of Degrees with Applications to Bifurcations and Differential Equations, Wiley, New York, 1996.
17. X. Liao, Absolute Stability of Nonlinear Control Systems, Kluwer Academic/China Science Press, 1993.
18. Y.K. Li, Positive periodic solution for neutral delay model, Acta Math. Sinica 39 (1996) 789-795.
19. H.I. Freedman, J.B. Shukla, Models for the effect of toxicant in single species and predator-prey system, J. Math. Biol. 30 (1991) 15-30.
20. T.G. Hallam, C.E. Clark, R.R. Lassider, Effects of toxicants on populations, A qualitative approach I: Equilibrium environmental exposure, Ecol. Modelling 8 (1983) 291-304.
21. T.G. Hallam, C.E. Clark, G.S. Jordan, Effects of toxicants on populations, A qualitative approach II: First order kinetics, J. Math. Biol. 18 (1983) 25-37.
22. T.G. Hallam, J.T. Deluna, Effects of toxicants on populations, A qualitative approach III: Environmental and food chain pathways, J. Theory Biol. 109 (1984) 411-429.
23. E.C. Pielou, An Introduction to Mathematical Ecology, Wiley, New York, 1969.
24. K. Gopalsamy, X. He, L. Wen, On a periodic neutral logistic equation, Glasgow Math. J. 33 (1991) 281-286.
25. K. Gopalsamy, B.G. Zhang, On a periodic neutral logistic equation, Dynam. Stability Systems 2 (1988) 183-195.
26. B.G. Zhang, K. Gopalsamy, Global attractivity and oscillations in a periodic logistic equation, J. Math. Anal. Appl. 150 (1990) 274-283.
27. R.E. Gaines, J. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977.