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Models for optimal harvest with convex function of growth rate of a population

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Abstract

Two models for growth of a population, which are described by a Cauchy problem for an ordinary differential equation with right-hand side depending on the population size and time, are investigated. The first model is time-discrete, i.e., the moments of harvest are fixed and discrete. The second model is time-continuous, i.e., a crop is harvested continuously in time. For autonomous systems, the second model is a particular case of the variational model for optimal control with constraints investigated in [1]. However, the prerequisites and the method of investigation are somewhat different, for they are based on Lemma1 presented below. In this paper, the existence and uniqueness theorem for the solution of the discrete and continuous problems of optimal harvest is proved, and the corresponding algorithms are presented. The results obtained are illustrated by a model for growth of the light-requiring green alge Chlorella. Bibliography: 6 titles.

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References

  1. R. E. Bellman, I. Glicksberg, and O. A. Gross,Some aspects of the mathematical theory of control processes, Rand Corporation, Santa Monica (1958).

    Google Scholar 

  2. K. E. F. Watt,Ecology and Resource Management. A Quantitative Approach, McGraw-Hill Book Company, New York-San Francisco-St. Louis-Toronto-London-Sydney (1968).

    Google Scholar 

  3. Yu. M. Sviryezhev and Ye. Ya. Yelizarov, “Mathematical modeling of biological systems,”Prbl. Kosm. Biol.,20 (1972).

  4. A. B. Gorostko and G. A. Ugol’nitsky,Introduction to the Modeling of Ecological and Economic Systems [in Russian], Rostov University Press (1990).

  5. V. N. Belyanin and B. G. Kovrov, “A mathematical model for biosynthesis in a light-limited culture of micro-organisms,”Dokl. Acad. Nauk SSSR,179 No. 6 (1968).

    Google Scholar 

  6. I. N. Lyashenko and Sh. R. Redzhepova,Mathematical Modeling and Optimal Design of Some Economic Solar-Power-Engineering Systems [in Russian], Ylym, Ashkhabad (1989).

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Authors
  1. O. I. Lyashenko
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Additional information

Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 77, 1993, pp. 75–86.

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Lyashenko, O.I. Models for optimal harvest with convex function of growth rate of a population. J Math Sci 77, 3445–3451 (1995). https://doi.org/10.1007/BF02367992

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  • DOI: https://doi.org/10.1007/BF02367992

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