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- Title
Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level.
- Authors
Hasibuan, Arjun; Supriatna, Asep Kuswandi; Rusyaman, Endang; Biswas, Md. Haider Ali
- 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.
- Subjects
LIMIT cycles; BIOMASS; MARINE parks &; reserves; HARVESTING; FOREST biomass; EQUILIBRIUM
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 18, p4015
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11184015