Michaelis-Menten Models with Constant Harvesting of Restricted Prey Populations Minimum Place and Amount Capacity

Authors

  • Aswar Anas Universitas PGRI Argopuro, Jember, Indonesia
  • Marsidi Universitas PGRI Argopuro, Jember, Indonesia

DOI:

https://doi.org/10.15642/mantik.2021.7.2.107-114

Keywords:

Food chain model, Michaelis-Menten model, Prey-predator model

Abstract

Food chain modeling is currently developing rapidly. The ecosystem is protected from the chain of eating and eating processes. All living things need each other, but if the process of eating them is not balanced, then the extinction of living things will occur. One of them is the prey and predator model that serves as a balancer in the food chain system. The Michaelis-Menten model is a prey-predator model that essentially prevents prey extinction. The problem is how to keep the prey from becoming extinct but with maximum harvesting in one place and the minimum amount of prey at the right time. The method used to overcome this problem is to add two new variables to the Michaelis-Menten model, namely the minimum number of prey and the capacity of the place to be occupied. It is seen that the system will be in equilibrium if the predator mortality rate is large so that the prey is kept from extinction until harvesting. In addition, the right time for good breeding can also be determined. From this model, it is found that the right time for harvesting so that prey extinction does not occur is Capture.PNG

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Author Biography

Marsidi, Universitas PGRI Argopuro, Jember, Indonesia

 

 

References

S. O. Lehtinen, “Ecological and evolutionary consequences of predator-prey role reversal: Allee effect and catastrophic predator extinction,” J. Theor. Biol., vol. 510, p. 110542, 2021, DOI: 10.1016/j.jtbi.2020.110542.

X. Dongmei and J. Leslie Stephen, “Bifurcation Of A Ratio Dependent Predator-Prey System With Constant Rate Harvesting,” vol. 65, no. 3, pp. 737–753, 2013.

A. Mapunda, E. Mureithi, N. Shaban, and T. Sagamiko, “Effects of Over-Harvesting and Drought on a Predator-Prey System with Optimal Control,” Open J. Ecol., vol. 08, no. 08, pp. 459–482, 2018, doi: 10.4236/oje.2018.88028.

H. Shim, T. Operations, and S. Korea, “Visualization and Interaction Design for Ecosystem Modeling Introduction Background Lotka-Volterra Model and Textual Modeling Two-Dimensional System Dynamics Modeling Three-Dimensional Integrative Modeling Summary Further Reading,” pp. 3685–3693, 2008.

S. Marom, “Pembentukan Model Mangsa Pemangsa Dengan Pemanenan Mangsa,” vol. 1, no. 2, pp. 181–187, 2013.

A. Anas, “Model Pemangsa dan Mangsa lotka Voltera Proporsional terhadap Model Logistik Von Bertallanfy Termodifikasi,” Al-Fitrah, vol. 12, pp. 101–116, 2017.

T. Henny M, U. R. Heri Selistyo, and W. Widowati, “Model Pertumbuhan Logistik Dengan Waktu Tunda,” J. Mat., vol. 11, pp. 43–51, 2008.

A. Tsoularis and J. Wallace, “Analysis of logistic growth models,” Math. Biosci., vol. 179, no. 1, pp. 21–55, 2002, doi: 10.1016/S0025-5564(02)00096-2.

D. Xiao and S. Ruan, “Global dynamics of a ratio-dependent predator-prey system,” vol. 290, no. 10071027, pp. 268–290, 2001.

M. Robert, Worldwide Differential Equations with Linear Algebra. Worldwide Center of Mathematics, LLC, 2012.

A. Keng Ceng, Differential Equations: Models and Methods. McGraw-Hill Education, 2005.

C. H. Edwards and D. E. Penney, Elementary Differential Equation.

H. Anton and C. Rorres, Elementary Linear Algebra with Applications. John Wiley & Sons, INC., 2005.

J. Stewart, Calculus. Thomson Learning, Inc, 2008.

T. PNV, Dynamical System, An Introduction with Application in Economics and Biology. Springer- Verlag. Heidelberg, Germany, 1994.

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Published

2021-10-31

How to Cite

Aswar Anas, & Marsidi. (2021). Michaelis-Menten Models with Constant Harvesting of Restricted Prey Populations Minimum Place and Amount Capacity. Jurnal Matematika MANTIK, 7(2), 107–114. https://doi.org/10.15642/mantik.2021.7.2.107-114

Issue

Vol. 7 No. 2 (2021): Mathematics and Applied Mathematics

Section

Articles

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