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ISSN:2325-6192 (print)
ISSN:2325-6206 (online)
Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn

Fishery Type Based Prey-Predator Optimal Harvesting Model under Intuitionistic Fuzzy Environment

Journal of Environmental Accounting and Management 11(3) (2023) 307--327 | DOI:10.5890/JEAM.2023.09.005

M. Mukherjee$^{1}$, D. Pal$^{2}$, S. K. Mahato$^{1}$

$^{1}$ Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, West Bengal, 723104, India

$^{2}$ Chandrahati Dilip Kumar High School (H.S.), Chandrahati, West Bengal, 712504, India

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Abstract

Depending upon Lotka-Volterra model along with biological parameters, intuitionistic fuzzy in nature, this paper deals with harvesting system of prey species and predator species. Our aim is to analyze the prey-predator model whose numerical values are imprecise in nature. To get rid of the vagueness, we use the concept of triangular intuitionstic fuzzy numbers. We first develop the crisp model under some important assumptions. Then the crisp model is transformed into intuitionistic fuzzy model by using the concept of Hukuhara derivative and then it is crispified with the help of Yager's Ranking method. We investigate existence of the equilibrium points of above mentioned crispified system and the condition of the local stability of those points is obtained by analyzing the eigen values of the variational matrix. Then the condition of global stability is described by using suitable Lyapunov function. The economic aspects along with the harvesting policies at optimal stage are described. The existence of the limit cycle of the fuzzy prey-predator model is analyzed by using Bendixon-Dulac-test. Furthermore, numerical simulations are presented in tabular form and graphical form to support the theoretical results.

Acknowledgments

The authors would like to express their gratitude to the Editor Dimitri Volchenkov, and the anonymous Referees for their encouraging and constructive comments for the improvement of the manuscript.

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