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

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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.

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References

  1. Aiello, W.G., Freedman, H.I. A time–delay model of single–species growth with stage structure. Math. Biosci., 101:139–153 (1990)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  5. Cui, J., Chen, L. The effect of dispersal on the time varying logistic population growth. Computers Math. Applic., 36(3):1–9 (1998)

    Article  Google Scholar 

  6. Hale, J.K. Theory of functional differential equations. Springer–Verlag, Berlin, 1977

  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)

    Article  MathSciNet  Google Scholar 

  8. Lancaster, P., Tismenetsky, M. The theory of matrices. Second Edition, Academic Press, New York, 1985

  9. Levin, S.A. Dispersion and population interactions. Am. Nat., 1974, 108:207–228 (1974)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  11. Smith, H.L. Monotone semiflow, generated by functional differential equations. J. Differential Equation, 66:420–442 (1987)

    Article  Google Scholar 

  12. Smith, H.L. Monotone dynamical system:an introduction to the theory of competitive and cooperative system. American Mathematical Society, Providence, Rhode Island, 1995

  13. Takeuchi, Y. Cooperative system theory and global stability of dispersal models. Acta Appl. Math., 14:49–57 (1982)

    Article  Google Scholar 

  14. Wang, W., Fergola, P., Tenneriello, C. Global attractivity of periodic solutions of population models. J. Math. Anal. Appl., 211:498–511 (1997)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Computer Network Information Center, Chinese Academy of Sciences, Beijing, 100080, China

    Zhong-hua Lu & Xue-bin Chi

  2. Department of mathematics, Xi’an University of Finance and Economics, Xi’an, 710061, China

    Zhong-hua Lu

  3. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China

    Lan-sun Chen

Authors
  1. Zhong-hua Lu
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  2. Xue-bin Chi
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  3. Lan-sun Chen
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Corresponding author

Correspondence to Zhong-hua Lu.

Additional information

Supported by the Special Fund for Major State Basic Research Projects (973, G1999032805), National Hitech Program (863, No.2002AA104540), Postdoctor Fund of China (No. 2003033243), the National Natural Science Foundation of China (No. 10171106).

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Lu, Zh., Chi, Xb. & Chen, Ls. Global Attracting Behavior of Non-autonomous Stage-structured Population Dynamical System with Diffusion. Acta Mathematicae Applicatae Sinica, English Series, English Series 19, 467–476 (2003). https://doi.org/10.1007/s10255-003-0122-2

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  • DOI: https://doi.org/10.1007/s10255-003-0122-2

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