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Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level

Arjun Hasibuan, Asep Kuswandi Supriatna (a.k.supriatna@unpad.ac.id), Endang Rusyaman and Md. Haider Ali Biswas
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Arjun Hasibuan: Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
Asep Kuswandi Supriatna: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
Endang Rusyaman: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
Md. Haider Ali Biswas: Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh

Mathematics, 2023, vol. 11, issue 18, 1-16

Abstract: In this work, we examine a predator–prey model that considers the implicit marine reserve in prey species and a linear function of critical biomass level. The model’s basic properties (existence, uniqueness, positivity, boundedness, and permanence) and equilibrium points are determined. We obtain three equilibrium points: the trivial equilibrium point, the equilibrium point where there is no harvest, and the co-existing equilibrium point. The local and global stability of each equilibrium point of the model is explored. Moreover, the interior equilibrium point is always globally asymptotically stable, and the system experiences no limit cycles around the interior equilibrium point. Numerical simulations are conducted to illustrate the theoretical results obtained. Finally, we find overlapping conditions regarding the dynamics between the model we developed and a model that considers a constant critical biomass level for certain parameters.

Keywords: marine reserve; linear harvesting; stability; predator–prey; critical biomass (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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