Conservation of a Prey Species Through Optimal Taxation: A Model with Beddington–DeAngelis Functional Response

Moulipriya Sarkar (), Tapasi Das and R. N. Mukherjee
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Moulipriya Sarkar: Heritage Institute of Technology
Tapasi Das: University Institute of Technology, Burdwan University
R. N. Mukherjee: Burdwan University

Chapter Chapter 9 in Applications of Operational Research in Business and Industries, 2023, pp 125-140 from Springer

Abstract: Abstract The selective harvesting of prey population is discussed in the given article. Here, both prey and predator receive the functional response of Beddington–DeAngelis. Only a fraction of the prey species is allowed to be accessed by the predator. The study of the positivity of the solutions of the system of linear equations is made along with the existence of various equilibrium points and their stability. If the environmental carrying capacity of the prey species is used as bifurcation parameter, a Hopf bifurcation around the interior equilibrium may occur. Pontryagin’s maximal principle is used to solve the problem of optimal taxation policy. The outputs of the proposed model are illustrated and verified with numerical examples using Maple.

Keywords: Stability; Catchability coefficient; Harvesting; Hopf bifurcation; Carrying capacity; Pontryagin’s maximum principle; 92B05; 92B10 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnopch:978-981-19-8012-1_9

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DOI: 10.1007/978-981-19-8012-1_9

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