Acta Mathematicae Applicatae Sinica, English Series

, Volume 19, Issue 3, pp 499–504 | Cite as

The Effect of Dispersal on Population Growth with Stage-structure

Original papers


The effect of dispersal on the permanence of population in a polluted patch is studied in this paper. The authors constructed a single-species dispersal model with stage-structure in two patches. The analysis focuses on the case that the toxicant input in the polluted patch has a limit value. The authors derived the conditions under which the population will be either permanent, or extinct.


Patch environment stage-structure pollution dispersal permanence 

2000 MR Subject Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aiello, W.G., Freedman, H.I. A time delay model of single–species growth with stage structure. Math. Biosci, 101:139–152 (1990)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Berreta E., Takeuchi, Y. Global asymptotic stability of Lotka–Volterra diffusion models with continuous time delays. SIAMJ. Appl. Math., 48:627–651 (1988)CrossRefGoogle Scholar
  3. 3.
    Cui, J., Chen, L., Wang, W. The effect of dispersal on population growth with stage–structure. Computers Math. Applic., 39:91–102 (2000)CrossRefGoogle Scholar
  4. 4.
    Freedman, H.I. Single species migration in two habitats:persistence and extinction. Mathl. Modelling, 8:778–780 (1987)CrossRefGoogle Scholar
  5. 5.
    Freedman, H.I., Takechi, Y. Predator survival versus extinction as a function of dispersal in a predator–prey model with patchy environment. Nonli. Anal., 13:993–1002 (1989)CrossRefGoogle Scholar
  6. 6.
    Hirsh, M.W. The dynamical systems approach to differential equations. Bull. A.M.S., 11:1–64 (1984)CrossRefGoogle Scholar
  7. 7.
    Lancaster, P., Tismenetsky, M. The Thoery of Matrices, second edition. Academic Press, Orlando, 1985Google Scholar
  8. 8.
    Leung, A. Limiting behavior for a prey–predator model with diffusion and crowding effects. J. Math. Biol., 6:87–93 (1978)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lu, Zhengyi, Takechi, Y. Permanence and global stability for cooperative Lotka–Volterra diffusion systems. Nonli. Anal., 10:963–975 (1992)CrossRefGoogle Scholar
  10. 10.
    Mahbuba, R., Chen, L.S. On the non–autonomous Lotka–Volterra competition system with diffusion. Differential Equations and Dynamical System, 2:243–253 (1994)Google Scholar
  11. 11.
    Rothe, F. Convergence to the equilibrium state in the Volterra–Lotka diffusion equations. J. Math. Biol., 3:319–324 (1976)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Skellam, J.D. Random dispersal in theoretical population. Biometrika, 38:196–218 (1951)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Takechi, Y. Cooperative system theory and global stability of dispersal models. Acta Appl. Math., 14:49–57 (1989)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Wang, W., Chen, L. Global stability of a population dispersal in a two–patch environment. Dynamical Systems and Applications, 6:207–216 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Institute of Applied MathematicsAcademy of Mathematics and System Sciences, Chinese Academy of SciencesBeijingChina
  2. 2.Department of MathematicsInner Mongolia UniversityHuhhotChina

Personalised recommendations