A single species model with impulsive diffusion

Acta Mathematicae Applicatae Sinica

Volumn 21, Issue 1, 2005, Pages 43-48

  Hui, Jing ^a,b   Chen, Lan Sun ^c  

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b GUANGXI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 16244366784     PISSN: 01689673     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10255-005-0213-3     Document Type: Article

References (21)

1. Bainov, D., Simeonov, P. Impulsive di.erential equations: periodic solution and applications. Longman, London, 1993
2. Beretta, E., Takeuchi, Y. Global asymptotic stability of lotka-volterra di.usion models with continuous time delays. SIAM J. Appl. Math., 48: 627-651 (1988)
3. Beretta, E., Takeuchi, Y. Global stability of single species di.usion volterra models with continuous time delays. Bull. Math. Biol., 49: 431-448 (1987)
4. Freedman, H.I., Takeuchi, Y. Global stability and predator dynamics in a model of prey dispersal in a patchy environment. Nonlinear Anal., 13: 993-1002 (1989)
5. Freedman, H.I. Single species migration in two habitats: persistence and extinction. Math. Model., 8: 778-780 (1987)
6. Freedman, H.I., Rai, B., waltman, P. Mathematical models of population interactions with dispersal ii: di.erential survival in a change of habitat. J. Math. Anal. Appl., 115: 140-154 (1986)
7. Freedman, H.I., Takeuchi, Y. Predator survival versus extinction as a function of dispersal in a predatorprey model with patchy environment. Appl. Anal., 31: 247-266 (1989)
8. Freedman, H.I., Waltman, P. Mathematical models of population interaction with dispersal I: stability of two habitats with and without a predator. SIAM J. Appl. Math., 32: 631-648 (1977)
9. Hastings, A. Dynamics of a single species in a spatially varying environment: the stability role of high dispersal rates. J. Math. Blol., 16: 49-55 (1982)
10. Holt, R.D. Population dynamics in two patch environments: some anomalous consequences of optional habitat selection. Theor. Pop. Biol., 28: 181-208 (1985)
11. Funasaki, E., Kot, M. Invasion and chaos in a periodically pulsed mass-action chemostat. Theor. Pop. Blol., 44: 203-224 (1993)
12. Kuang, Y., Takeuchi, Y. Predator-prey dynamics in models of prey dispersal in two patch environments. Math. Biosci., 120: 77-98 (1994)
13. Levin, S.A. Dispersion and population interactions. Amer. Natur., 108: 207-228 (1974)
14. Lakmeche, A., Arino, O. Bifurcation of nontrivial periodic solution of impulsive di.erential equations arising chemotherapeutic treatment. Dynamics of Continuous, Discrete and Impulsive system, 7: 265-287 (2000)
15. Levin, S.A. Spatial patterning and the structure of ecological communities, in some mathematical questions in biology. VII, Vol. 8, Amer. Math. Soc., Providence, RI, 1976
16. Liu, X. Impulsive stabilization and applications to population growth models. J. Math., 25 (1) : 381-395 (1995)
17. Liu, X., Zhang, S. A cell population model described by impulsive pdes-existence and numerical approximation. Comput. Math. Appl., 36(8): 1-11 (1998)
18. Liu, X., Rohof, K. Impulsive control of a lotka-volterra system. IMA Journal of Mathematical Control & Information, 15: 269-284 (1998)
19. Lu, Z.Y., Takeuchi, Y. Permanence and global stability for cooperative lotka-volterra di.usion systems. Nonlinear Anal., 10: 963-975 (1992)
20. Shulgin, B., Stone, L. et al. Pulse vaccination strategy in the sir epidemic model. Bull. Math. Biol., 60: 1-26 (1998)
21. Smith, H.L. Cooperative systems of di.erential equations with concave nonlinearities. Nonlinear Anal. TMA, 10: 1037-1052 (1986)