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A Mathematical Model for Optimal Management and Utilization of a Renewable Resource by Population

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  • B. Dubey
  • Atasi Patra

Abstract

A dynamical model is proposed and analyzed to study the effect of the population on the resource biomass by taking into account the crowding effect. Biological and bionomical equilibria of the system are discussed. The global stability behavior of the positive equilibrium is studied via the output feedback control. An appropriate Hamiltonian function is formed for the discussion of optimal harvesting of resource which is utilized by the population using Pontryagin's Maximum Principal. A numerical simulation is performed on the model to analyze the theoretical results.

Suggested Citation

  • B. Dubey & Atasi Patra, 2013. "A Mathematical Model for Optimal Management and Utilization of a Renewable Resource by Population," Journal of Mathematics, Hindawi, vol. 2013, pages 1-9, January.
    • Handle: RePEc:hin:jjmath:613706
    DOI: 10.1155/2013/613706
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    References listed on IDEAS

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    1. Leung, Anthony & Wang, Ar-Young, 1976. "Analysis of Models for Commercial Fishing: Mathematical and Economical Aspects," Econometrica, Econometric Society, vol. 44(2), pages 295-303, March.
    2. Ragozin, David L. & Brown, Gardner Jr., 1985. "Harvest policies and nonmarket valuation in a predator -- prey system," Journal of Environmental Economics and Management, Elsevier, vol. 12(2), pages 155-168, June.
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    Cited by:

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