Analisis Kestabilan Model Mangsa Pemangsa dengan Pemanenan Ambang Batas pada Populasi Pemangsa
DOI:
https://doi.org/10.20956/jmsk.v16i1.6575Keywords:
Prey-predator model threshold harvesting, equibrium pointAbstract
Abstrak
Penelitian ini mengkaji model satu mangsa dan satu pemangsa yang saling berkompetisi. Fungsi predasi dari pemangsa diasumsikan menggunakan fungs1 respon Holling tipe II. Dengan asumsi bahwa adanya kompetisi intraspesifik pada popuasi pemangsa serta dilakukan pemanenan ambang batas pada popuasi pemangsa. Pada model tersebut dilakukan analisis tentang syarat kewujudan dan kestabilan titik keseimbangan interior. Analisis kestabilan titik keseimbangan interior dilakukan dengan metode linearisasi dan dengan memperhatikan nilai eigen dari matriks Jacobi yang diperoleh. Terdapat sepuluh titik kesetimbangan yang diperoleh pada model, satu diantaranya dapat dinterpretasikan. Titik tersebut dinyatakan stabil asimtotik. Berdasarkan hasil anasis menggunakan beberapa parameter, diketahui bahwa ada suatu waktu pemanenan ambang batas harus dihentikan karna sudah tidak memenuhi syarat kriteria ambang batas yang telah ditentukan.
Kata kunci : Model mangsa pemangsa, Pemanenan ambang batas, Titik kesetimbangan
Abstract
This study examines the model of one prey and one predator who mutates each other. The predation function of predators is assumed to use the Holling type II response function. Assuming that the existence of intraspecific competition in predatory population and theshold harvesting for predatory population is carried out. In this model, an analysis of the actual conditions and stability of the interior balance point is carried out. Analysis of the interior stability balance points was carried out by linearization method and by taking into account the eigenvalues of the Jacobian matrix obtained. There are ten equilibrium points of engagement obtained on the model, one of which can be interpreted. This point is stated as asymptotically stable. Based on the results of analysis using several parameters, it is known that there is a time when harvesting the threshold must be stopped because it has not fulfill the specified criteria for threshold.
Keyword : Prey-predator model threshold harvesting, equibrium point
References
Saenz, R.A. dan Hethcote, H.W., 2006. Competing Species Models with an Infectious Disease, J. Math. Biosci. Eng. 3 (1):219–235
Toaha. S., 2013. Pemodelan Matematika Dalam Dinamika Populasi. Dua Satu Press: Makassar.
Ali N., Haque M., Venturino E. dan Chakravarty S., 2017. Dynamics of a Three Species Ratio-Dependent Food Chain Model with Intra-Specific Competition within The Top Predator. Computers in Biology and Medicine. 85: 63-74.
Leard, B dan Rebaza, J., 2010. Analysis of Predator-Prey Models with Continuous Threshold Harvesting. Applied Mathematics and Computation. 217 : 5265-5278.
Waluya, S.T., 2011. An Introduction to Differential Equations. Unnes Press: Semarang.
Liu, Z. dan Tan, R., 2007. Impulsive Harvesting and Ttocking in a Monod–Haldane Functional Response Predator–Prey System. Chaos, Solitons and Fractals. 34: 454–464.
Lv.Y, Yuan R.dan Pei Y., 2013. Dynamic in Two Nonsmooth Predator-Prey Models with Threshold Harvesting. Springer-Verlag.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license. This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.
