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

In: Applications of Operational Research in Business and Industries

Author

Listed:
  • Moulipriya Sarkar

    (Heritage Institute of Technology)

  • Tapasi Das

    (University Institute of Technology, Burdwan University)

  • R. N. Mukherjee

    (Burdwan University)

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.

Suggested Citation

  • Moulipriya Sarkar & Tapasi Das & R. N. Mukherjee, 2023. "Conservation of a Prey Species Through Optimal Taxation: A Model with Beddington–DeAngelis Functional Response," Lecture Notes in Operations Research, in: Angappa Gunasekaran & Jai Kishore Sharma & Samarjit Kar (ed.), Applications of Operational Research in Business and Industries, chapter 0, pages 125-140, Springer.
    • Handle: RePEc:spr:lnopch:978-981-19-8012-1_9
    DOI: 10.1007/978-981-19-8012-1_9
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