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Discontinuity, Nonlinearity, and Complexity 12(3) (2023) 655--671 | DOI:10.5890/DNC.2023.09.012

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

$^{1}$ Chandrahati Dilip Kumar High School (H.S.), Chandrahati, West Bengal, 712504, India

$^{2}$ Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, West Bengal, 723104, India

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Abstract

In this study, a Lotka-Volterra type prey-predator harvesting model with fuzzy biological parameters under some assumptions is presented. It is assumed that the parameters involved in biological model are vague/imprecise under consideration. The uncertainty of the said parameters is handled by triangular fuzzy numbers. First, the crisp harvesting model is formulated under some assumptions. Then the crisp model is converted to fuzzy model and then it is defuzzified by using utility function method. The existences of equilibrium points of the defuzzified model are identified and corresponding stabilities are checked.\ The economic features as well as the harvesting strategies at the optimal stage of our wished-for model is considered. Lastly, mathematical simulations of the defuzzified model with numerical data are carried out using MATLAB and MATHEMATICA to validate the theoretical results.

Acknowledgments

\bibitem{Lotka} Lotka, A.J. (1925), \textit{Elements of physical Biology}, Williams and Wilkins, Baltimore: New York.

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