Skip to main content
SpringerLink
Log in

An optimal policy for a fish harvest

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

A dynamical model for harvesting a fish population system is proposed by introducing control into the known Verhulst-Pearl model. An optimal control problem including some parameters is stated, and the usual necessary conditions are applied. For specific parameter values, the candidate control policy is deduced, and optimality is verified by applying a sufficiency theorem. The optimal trajectories may contain maximum and minimum control arcs as well as a singular subarc. The significance of the singular arc is interpreted in terms of the system dynamics.

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. Intriligator, M. D.,Mathematical Optimization and Economic Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1971.

    Google Scholar 

  2. Shell, K.,Applications of Pontriagin's Maximum Principle to Economics, Mathematical Systems Theory and Economics, Edited by H. W. Kuhn and G. P. Szego, Springer-Verlag, Berlin, Germany, 1969.

    Google Scholar 

  3. Ho, Y. C.,Control Theory, Applied Mathematics, and Engineering, Journal of Dynamic Systems, Measurement, and Control, ASME Transactions, Vol. 93, Series G, pp. 131–133, 1971.

    Article  Google Scholar 

  4. Goh, B. S.,Optimal Control of a Fish Resource, Malayan Scientist, Vol. 5, pp. 65–70, 1969/70.

    Google Scholar 

  5. Vincent, T. L.,Pest Management Programs via Optimal Control Theory, Proceedings of the Joint Automatic Control Conference, Stanford, California, 1972.

  6. Spear, R. C., andWet, E. Dynamic Aspects of Environmental Toxicology, Journal of Dynamic Systems, Measurements, and Control, ASME Transactions, Series G, Vol. 94, pp. 114–118, 1972.

    Article  Google Scholar 

  7. Taylor, H. M.,Some Models in Epidemic Control, Mathematical Biosciences, Vol. 3, pp. 383–398, 1968.

    Article  Google Scholar 

  8. Verhulst, P. F.,Recherches Mathématiques sur la Loi d'Accroissement de la Population, Mémoires de l'Académie Royale de Bruxelles, Vol. 43, pp. 1–58, 1844.

    Google Scholar 

  9. Pearl, R.,Studies in Human Biology, Williams and Wilkins, New York, New York, 1924.

    Google Scholar 

  10. Leitmann, G.,Introduction to Optimal Control, McGraw-Hill Book Company, New York, New York, 1966.

    MATH  Google Scholar 

  11. Leitmann, G.,Sufficiency Theorems for Optimal Control, Journal of Optimization Theory and Applications, Vol. 2, pp. 285–292, 1968.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

    E. M. Cliff (Assistant Professor)

  2. Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona

    T. L. Vincent (Professor)

Authors
  1. E. M. Cliff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. L. Vincent
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by G. Leitmann

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cliff, E.M., Vincent, T.L. An optimal policy for a fish harvest. J Optim Theory Appl 12, 485–496 (1973). https://doi.org/10.1007/BF00935243

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00935243

Keywords

Search

Navigation