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Harvesting in a two-prey one-predator fishery: a bioeconomic model

  • T. K. Kar (a1) and K. S. Chaudhuri (a2)
  • DOI: http://dx.doi.org/10.1017/S144618110001347X
  • Published online: 01 February 2009
Abstract
Abstract

A multispecies harvesting model with interference is proposed. The model is based on Lotka-Volterra dynamics with two competing species which are affected not only by harvesting but also by the presence of a predator, the third species. In order to understand the dynamics of this complicated system, we choose to model the simplest possible predator response function in which the feeding rate of the predator increases linearly with prey density. We derive the conditions for global stability of the system using a Lyapunov function. The possibility of existence of a bioeconomic equilibrium is discussed. The optimal harvest policy is studied and the solution is derived in the equilibrium case using Pontryagin's maximal principle. Finally, some numerical examples are discussed.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]K. S. Chaudhuri , “A bioeconomic model of harvesting a multispecies fishery”, Ecol. Model. 32 (1986) 267279.

[2]K. S. Chaudhuri , “Dynamic optimization of combined harvesting of a two species fishery”, Ecol. Model. 41 (1988) 1725.

[3]K. S. Chaudhuri and T. Johnson , “Bioeconomic dynamics of a fishery modelled as an S-system”, Math. Biosci. 99 (1990) 231249.

[4]K. S. Chaudhuri and S. Saha Ray , “On the combined harvesting of a prey predator system”, J. Biol. Syst. 4 (1996) 376389.

[8]J. D. Murray , Mathematical Biology (Springer, Berlin, 1993).

[10]D. L. Ragozin and G. Brown , “Harvest policies and non-market valuation in a predator-prey system”, J. Envirn. Econ. Manag. 12 (1985) 155168.

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The ANZIAM Journal
  • ISSN: 1446-1811
  • EISSN: 1446-8735
  • URL: /core/journals/anziam-journal
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