Skip to main content
Log in

The Effect of Dispersal on Population Growth with Stage-structure

  • Original papers
  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aiello, W.G., Freedman, H.I. A time delay model of single–species growth with stage structure. Math. Biosci, 101:139–152 (1990)

    Article  MathSciNet  Google Scholar 

  2. Berreta E., Takeuchi, Y. Global asymptotic stability of Lotka–Volterra diffusion models with continuous time delays. SIAMJ. Appl. Math., 48:627–651 (1988)

    Article  Google Scholar 

  3. Cui, J., Chen, L., Wang, W. The effect of dispersal on population growth with stage–structure. Computers Math. Applic., 39:91–102 (2000)

    Article  Google Scholar 

  4. Freedman, H.I. Single species migration in two habitats:persistence and extinction. Mathl. Modelling, 8:778–780 (1987)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  6. Hirsh, M.W. The dynamical systems approach to differential equations. Bull. A.M.S., 11:1–64 (1984)

    Article  Google Scholar 

  7. Lancaster, P., Tismenetsky, M. The Thoery of Matrices, second edition. Academic Press, Orlando, 1985

  8. Leung, A. Limiting behavior for a prey–predator model with diffusion and crowding effects. J. Math. Biol., 6:87–93 (1978)

    Article  MathSciNet  Google Scholar 

  9. Lu, Zhengyi, Takechi, Y. Permanence and global stability for cooperative Lotka–Volterra diffusion systems. Nonli. Anal., 10:963–975 (1992)

    Article  Google Scholar 

  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. Rothe, F. Convergence to the equilibrium state in the Volterra–Lotka diffusion equations. J. Math. Biol., 3:319–324 (1976)

    Article  MathSciNet  Google Scholar 

  12. Skellam, J.D. Random dispersal in theoretical population. Biometrika, 38:196–218 (1951)

    Article  MathSciNet  Google Scholar 

  13. Takechi, Y. Cooperative system theory and global stability of dispersal models. Acta Appl. Math., 14:49–57 (1989)

    Article  MathSciNet  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yong-guang Yu.

Additional information

Supported by the National Nature Science Foundation of China (Grant No. 10171099).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, Yg., Zhang, Sc. & Yang, Zz. The Effect of Dispersal on Population Growth with Stage-structure. Acta Mathematicae Applicatae Sinica, English Series, English Series 19, 499–504 (2003). https://doi.org/10.1007/s10255-003-0126-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-003-0126-y

Keywords

2000 MR Subject Classification

Navigation