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Acta Mathematicae Applicatae Sinica, English Series

, Volume 19, Issue 3, pp 467–476 | Cite as

Global Attracting Behavior of Non-autonomous Stage-structured Population Dynamical System with Diffusion

Original papers
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Abstract

A non-autonomous single species dispersal model is considered, in which individual member of the population has a life history that goes through two stages, immature and mature. By applying the theory of monotone and concave operators to functional differential equations, we establish conditions under which the system admits a positive periodic solution which attracts all other positive solutions.

Keywords

Nonautonomous stage structure dispersal periodic solution global attractivity 

2000 MR Subject Classification

34C25 92D25 34D20 

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References

  1. 1.
    Aiello, W.G., Freedman, H.I. A time–delay model of single–species growth with stage structure. Math. Biosci., 101:139–153 (1990)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aiello, W.G., Freedman, H.I., Wu, J. Analysis of a model representing stage–structured population growth with state–dependent time delay. SIAM J. Appl. Math., 52(3):855–869 (1992)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Beretta, E., Takeuchi, Y. Global asymptotic stability of Lotka–Volterra diffusion models with continuous time delay. SIAM J. Appl. Math., 48:627–651 (1998)CrossRefGoogle Scholar
  4. 4.
    Cao, Y., Fan, J., Gard, T.C. The effects of state–structured population growth model. Nonlin. Anal. Th. Math. Appli., 16(2):95–105 (1992)CrossRefGoogle Scholar
  5. 5.
    Cui, J., Chen, L. The effect of dispersal on the time varying logistic population growth. Computers Math. Applic., 36(3):1–9 (1998)CrossRefGoogle Scholar
  6. 6.
    Hale, J.K. Theory of functional differential equations. Springer–Verlag, Berlin, 1977Google Scholar
  7. 7.
    Hastings, A. Dynamics of a single species in a spatially varying environment:the stabilizing role of high dispersal rates. J. Math. Biology, 16:49–55 (1982)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lancaster, P., Tismenetsky, M. The theory of matrices. Second Edition, Academic Press, New York, 1985Google Scholar
  9. 9.
    Levin, S.A. Dispersion and population interactions. Am. Nat., 1974, 108:207–228 (1974)CrossRefGoogle Scholar
  10. 10.
    Skellam, J.G. Random dispersal in theoretical population. Biometrika, 38:196–218 (1951)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Smith, H.L. Monotone semiflow, generated by functional differential equations. J. Differential Equation, 66:420–442 (1987)CrossRefGoogle Scholar
  12. 12.
    Smith, H.L. Monotone dynamical system:an introduction to the theory of competitive and cooperative system. American Mathematical Society, Providence, Rhode Island, 1995Google Scholar
  13. 13.
    Takeuchi, Y. Cooperative system theory and global stability of dispersal models. Acta Appl. Math., 14:49–57 (1982)CrossRefGoogle Scholar
  14. 14.
    Wang, W., Fergola, P., Tenneriello, C. Global attractivity of periodic solutions of population models. J. Math. Anal. Appl., 211:498–511 (1997)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Computer Network Information CenterChinese Academy of SciencesBeijingChina
  2. 2.Department of mathematicsXi’an University of Finance and EconomicsXi’anChina
  3. 3.Academy of Mathematics and System SciencesChinese Academy of SciencesBeijingChina

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