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Journal of Systems Science and Complexity

, Volume 20, Issue 3, pp 403–415 | Cite as

Optimal Birth Control for an Age-Dependent Competition System of N Species

  • Zhixue LuoEmail author
Article

Abstract

In this paper, we investigate optimal policies for an age-dependent n-dimensional competition system, which is controlled by fertility. By using Dubovitskii-Milyutin’s general theory, the maximum principles are obtained for the problems with free terminal states, infinite horizon, and target sets, respectively.

Keywords

Age-dependence optimal control population model system of partial differential equations the maximum principle 

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References

  1. 1.
    C. Rorres and W. Fair, Optimal age specific harvesting policy for continuous-time population model, Modeling and Differential Equations in Biology (ed. by T. A. Burton), Dekker, New York, 1980.Google Scholar
  2. 2.
    W. L. Chan and B. Z. Guo, Optimal birth control of population dynamics, Journal of Mathematical Analysis and Applications, 1989, 144(1): 532–552.CrossRefGoogle Scholar
  3. 3.
    W. L. Chan and B. Z. Guo, Optimal birth control of population dynamics, Part 2, Problems with free final time, phase constraints, and mini-max costs, Journal of Mathematical Analysis and Applications, 1990, 146(1): 523–539.CrossRefGoogle Scholar
  4. 4.
    S. Anita, Optimal harvesting for a nonlinear age-dependent population dynamics, Journal of Mathematical Analysis and Applications, 1998, 226(2): 6–22.CrossRefGoogle Scholar
  5. 5.
    B. Ainseba and M. Langlais, On a population dynamics control problem with age dependence and spatial structure, Journal of Mathematical Analysis and Applications, 2000, 248(2): 455–474.CrossRefGoogle Scholar
  6. 6.
    V. Barbu, M. Iannelli, and M. Martcheva, On the controllability of the Lotka-Mckendrick model of population dynamics, Journal of Mathematical Analysis and Applications, 2001, 253(2): 142–165.CrossRefGoogle Scholar
  7. 7.
    V. Barbu and M. Iannelli, Optimal control of population dynamics, Journal of Optimization Theory and Application, 1999, 102(1): 1–14.CrossRefGoogle Scholar
  8. 8.
    B. Z. Guo and G. Zhu, Control Theory of Population Distributional Parameter Systems (in Chinese), Press of Central China University of Science and Technology, Wuhan, China, 1999.Google Scholar
  9. 9.
    S. Anita, Analysis and Control of Age-Dependent Population Dynamics, Kluwer Academic Publishers, Dordrecht, 2000.Google Scholar
  10. 10.
    F. Albrecht, H. Gatzke, A. Haddad, and N. Wax, On the control of certain interacting populations, Journal of Mathematical Analysis and Applications, 1976, 53(1): 578–603.CrossRefGoogle Scholar
  11. 11.
    S. Lenhart, M. Liang, and V. Protopopescu, Optimal control of boundary habitat hostility for interacting species, Mathematical Methods in the Applied Sciences, 1999, 22(1): 1061–1077.CrossRefGoogle Scholar
  12. 12.
    L. G. Crespo and J. Q. Sun, Optimal control of populations of competing species, Nonlinear Dynamics, 2002, 27(1): 197–210.CrossRefGoogle Scholar
  13. 13.
    Zhixhe Luo, Ze-Rong He, and Wan-Tong Li, Optimal birth control for an age-dependent n-dimensional food chain model, Journal of Mathematical Analysis and Applications, 2003, 287(2): 557–576.CrossRefGoogle Scholar
  14. 14.
    I. V. Girsanov, Lectures on mathematical theory of extremum problem, in Lecture Notes in Economics and Mathematical Systems, Vol. 67, Springer-Verlag, Berlin, 1972.Google Scholar
  15. 15.
    M. Iannelli, Mathematical Theory of Age-Structured Population Dynamics, Giardini Editori E Stampatori in Pisa, 1994.Google Scholar

Copyright information

© Springer Science + Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsLanzhou Jiaotong UniversityLanzhouChina

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