Regulation of Combined Harvesting of a Prey-Predator Fishery with Low Predator Density by Taxation

Dr. Tarun Pradhan

doi:https://doi.org/10.14445/22315373/IJMTT-V54P533

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 54 | Number 4 | Year 2018 | Article Id. IJMTT-V54P533 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P533

Regulation of Combined Harvesting of a Prey-Predator Fishery with Low Predator Density by Taxation

Dr. Tarun Pradhan

Citation :

Dr. Tarun Pradhan, "Regulation of Combined Harvesting of a Prey-Predator Fishery with Low Predator Density by Taxation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 4, pp. 289-299, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P533

Abstract

In this paper, a model on prey-predator fishery is proposed and analyzed in which the predator density is low compared to the prey density. It is assumed that prey species obeys the logistic law of growth [1] and both the species are allowed to be harvested by the fishermen. In order to control over exploitation the regulatory agencies impose suitable taxes per unit of harvested biomass of landed fish. It is also assumed that the agencies impose a higher tax for harvesting predator fish species compared to the tax for harvesting prey fish species. Different efforts are given by the fishermen to harvest prey and predator species and the efforts are considered as dynamic variables. Different suitable ranges of taxes are determined for existence of all possible steady states. The local and global stability of the steady states are discussed. An optimal harvest policy has been discussed considering taxes as the control variables. All the results are illustrated with the help of a numerical example.

Keywords

prey-predator fishery, combined harvesting, regulatory agency, steady states, local and global stability, optimal harvest policy.

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