Efficiency Optimization for the Cyclic Use of a Renewable Resource

  • A. O. Belyakov
  • A. A. Davydov


We consider a periodic impulse harvesting of a renewable resource distributed in a domain of the arithmetic space and obeying the logistic growth low. We prove that, for a given harvesting effort, there exists an appropriate stationary distribution of the effort in the resource domain providing the maximum efficiency of the harvesting at infinite horizon, where the efficiency is the ratio of the harvesting profit to the total effort applied.


renewable resource logistic low harvesting effort cyclic process optimal exploitation. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. I. Arnol’d, “Optimization in mean and phase transitions in controlled dynamical systems,” Functional Anal. Appl. 36 (2), 83–92 (2002).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    A. O. Belyakov, A. A. Davydov, and V. M. Veliov, “Optimal cyclic exploitation of renewable resources,” J. Dyn. Control Syst. 21 (3), 475–494 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    A. A. Davydov, “Generic profit singularities in Arnold’s model of cyclic processes,” Proc. Steklov Inst. Math. 250, 70–84 (2005).MathSciNetzbMATHGoogle Scholar
  4. 4.
    A. A. Davydov and E. Mena Matos, “Generic phase transitions and profit singularities in Arnol’d’s model,” Sb. Math. 198 (1), 17–37 (2007).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    A. A. Davydov and T. S. Shutkina, “Optimizing a cyclic process with discount with respect to its time average profit,” Russ. Math. Surv. 64 (1), 136–138 (2009).CrossRefzbMATHGoogle Scholar
  6. 6.
    B. O. Koopman, “The theory of search. III. The optimum distribution of search effort,” Oper. Res. 5 (5), 613–626 (1957).MathSciNetCrossRefGoogle Scholar
  7. 7.
    O. Flaaten, “The optimal harvesting of a natural resource with seasonal growth,” Canad. J. Econ. 16 (3), 447–462 (1983).CrossRefGoogle Scholar
  8. 8.
    K. Erdlenbruch, A. Jean-Marie, M. Moreaux, and M. Tidball, “Cyclical versus non-cyclical harvesting policies in renewable resource management,” in Proceedings of the Monte Verità Conference on Sustainable Resource Use and Economic Dynamics, Monte Verita, Switzerland, 2008, pp. 1–34.Google Scholar
  9. 9.
    V. V. Zhikov, “Mathematical problems of search theory,” Tr. Vladimir. Politekh. Inst., 263–270 (1968).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia
  2. 2.National Research Nuclear University MEPhIMoscowRussia
  3. 3.National University of Science and Technology MISiSMoscowRussia

Personalised recommendations