Skip to main content
SpringerLink
Log in

Optimal Control of Populations of Competing Species

  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The optimal control problem of populations of two competing species isstudied by using the simple cell mapping method. Two control strategiesfor pursuing the extinction of one species are considered. The controlsinclude the inclusion of population of the other species from anexternal habitat and the parametric manipulation of the intrinsicgrowing rates of the targeted species. A control to maintain bothspecies alive in the long term is also studied by manipulating thecoupling coefficients.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kolosov, G. E., 'On a problem of control of the size of populations', Journal of Computer and Systems Sciences International 34(4), 1996, 115–122.

    Google Scholar 

  2. Pianka, E. R., Competition and Niche Theory, Sinauers Associates, Sunderland, MA, 1981.

    Google Scholar 

  3. Edelstein-Keshet, L., Mathematical Models in Biology, Random House, New York, 1988.

    Google Scholar 

  4. Murray, J., Mathematical Biology, Springer-Verlag, New York, 1989.

    Google Scholar 

  5. Kiyotaka, I., Hashem, M. M. A., and Keigo, W., 'Evolution strategy with competing subpopulations', in Proceedings of IEEE International Symposium on Computational Intelligence in Robotics and Automation, IEEE, New York, 1997, pp. 306–311.

    Google Scholar 

  6. Zhang, J., Chen, L., and Che, X. D., 'Persistence and global stability for two species nonautonomous competition Lotka-Volterra patch-system with time delay', Nonlinear Analysis 37, 1999, 1019–1028.

    Google Scholar 

  7. Hrinca, L., 'An optimal control problem for the Lotka-Volterra system with delay', Nonlinear Analysis, Theory, Methods and Applications 28(2), 1997, 247–262.

    Google Scholar 

  8. Hironori, H., 'Optimal control of nonlinear population dynamics', IEEE Transactions on Systems, Man and Cybernetics SMC-10(1), 1980, 32–38.

    Google Scholar 

  9. Suzanne, L., 'Optimal control of boundary habitat hostility for interacting species', Mathematical Methods in Applied Sciences 22(3), 1999, 1061–1077.

    Google Scholar 

  10. Chan, W. L. and Zhu, G. B., 'Overtaking optimal control problem of age-dependent populations with infinite horizon', Journal of Mathematical Analysis and Applications 150, 1990, 41–53.

    Google Scholar 

  11. Chan, W. L. and Zhu, G. B., 'Optimal birth control of population dynamics. II. Problems with free final time, phase constraints, and min-max costs', Journal of Mathematical Analysis and Applications 146, 1990, 523–539.

    Google Scholar 

  12. Hsu, C. S., 'A theory of cell-to-cell mapping dynamical systems', Journal of Applied Mechanics 47, 1980, 931–939.

    Google Scholar 

  13. Hsu, C. S., Cell-to-CellMapping, A Method of Global Analysis for Nonlinear Systems, Springer-Verlag, New York, 1987.

    Google Scholar 

  14. Hsu, C. S., 'A discrete method of optimal control based upon the cell state space concept', Journal of Optimization Theory and Applications 46(4), 1985, 547–569.

    Google Scholar 

  15. Bursal, F. H. and Hsu, C. S., 'Applications of a cell-mapping method to optimal control problems', International Journal of Control 49(5), 1989, 1505–1522.

    Google Scholar 

  16. Yen, J. Y., Chao, W. C., and Lu, S. S., 'Fuzzy cellmapping method for a sub-optimal control implementation', Control Engineering Practice 2(2), 1994, 247–254.

    Google Scholar 

  17. Wang, F. Y. and Lever, P. J. A., 'A cell mapping method for general optimum trajectory planning of multiple robotic arms', Robotics and Autonomous Systems 12, 1994, 15–27.

    Google Scholar 

  18. Crespo, L. G. and Sun, J. Q., 'Solution of fixed final state optimal control problems via simple cell mapping', Nonlinear Dynamics 23, 2000, 391–403.

    Google Scholar 

  19. Crespo, L. G. and Sun, J. Q., 'Solution of fixed final time optimal control problems vis simple cell mapping', Journal of Optimization Theory and Applications, 2000, submitted.

  20. Crespo, L. G. and Sun, J. Q., 'Effect of bifurcation on the semi-active optimal control problem', IEEE Transactions on Automatic Control, 2000, submitted.

  21. Crespo, L. G. and Sun, J. Q., 'Optimal control problem with target tracking and state constraints via simple cell mapping', Journal of Guidance and Control, 2000, in press.

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Delaware, Newark, DE, 19716, U.S.A

    L. G. Crespo & J. Q. Sun

Authors
  1. L. G. Crespo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Q. Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Crespo, L.G., Sun, J.Q. Optimal Control of Populations of Competing Species. Nonlinear Dynamics 27, 197–210 (2002). https://doi.org/10.1023/A:1014258302180

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014258302180

Search

Navigation