ANALISIS KESTABILAN MODEL INTERAKSI PREDATOR-PREY DENGAN FUNGSI RESPON MONOD-HALDANE DAN PERILAKU ANTI PEMANGSA

Muhammad Bachtiar Gaib, Wahdania At. Ja'a

Abstract


This article examines a competing prey-predator model using the Monod-Haldane response function and anti-predator behavior. This article discusses equilibrium point determination, equilibrium point stability analysis, and numerical simulation. Obtained three equilibrium points, namely T1, T2, and T3, where the equilibrium-point is always saddle, the stability of the equilibrium points T2 and T3 will be stable if it meets the predetermined parameter requirements. There are two cases in the equilibrium point where the first case is vertically stable and the second case is spiral stable.

Keywords


Predator-Prey Model; Response Function; Monod-Haldane; Anti Predators; Equilibrium Point

Full Text:

PDF

References


S. Saadah, A. Abadi, and D. Savitri, “Model Interaksi Mangsa Pemangsa Dengan Fungsi Respon Rasio Dependent Holling Tipe II dan Perilaku Anti Pemangsa,” MATHunesa Jurnal Ilmiah Matematika, vol.7, no.2, pp. 6-9, 2019.

P.B. Turchin, Complex Population Dynamics: A Theorical/Empirical Synthesis. New Jersey: Princeton University Press, 2003.

W. Widowati dan S. Sutimin, Buku Ajar Pemodelan Matematika, Semarang: UNDIP Press, 2007.

H.S. Panigoro, “Analisis Dinamik Sistem Predator-Prey Model Leslie-Gower dengan Pemanenan Secara Konstan Terhadap Predator,” J.Euler, vol.2, no.1, 1-12, 2014.

S.G. Mortoja, P. Panja, and S.K. Mondal, “Dynamics of a Predator-Prey Model with Stage-Structure on Both Species and Anti-Predator Behavior,” Informatics in Medicine Unlocked, vol.10, pp. 50-57, 2018. doi:https://doi.org/10.1016/j.imu.2017.12.004.

M. Agarwal, and R. Pathak, “Harvesting and Hopf Bifurcation in a Predator-Prey Model with Holling Type IV Functional Response,” International Journal of Mathematics and Soft Computing, vol.2, no.1, pp. 83-92, 2012.

S. Ruan, and D. Xiao, “Global Analysis in a Predator-Prey System with Nonmonotonic Functional Response,” SIAM J Appl Math, vol. 61, no.4, pp. 1445-1472, 2001.

W. Sokol, and J.A. Howell, “Kinetics of Phenol Oxidation by Washed Cells,” Biotechnol. Bio-eng., vol. 23, pp. 2039-2049, 1980.

S. H. Arsyad, R. Resmawan, and N. Achmad, “Analisis Model Predator-Prey Leslie-Gower dengan Pemberian Racun Pada Predator,” J. Ris. dan Apl. Mat., vol. 4, no. 1, pp. 1–16, 2020.

N. Hasan, R. Resmawan, and E. Rahmi, “Analisis Kestabilan Model Eko-Epidemiologi dengan Pemanenan Konstan pada Predator,” J. Mat. Stat. dan Komputasi, vol. 16, no. 2, pp. 121–142, Dec. 2020.

J.D. Logan, First Course in Differential Equations (Second Edition), New York: Springer-Verlag, 2010.

M.B. Gaib, Bifurkasi Hopf Pada Model Mangsa-Pemangsa Holling-Tanner Tipe II. Institut Pertanian Bogor, 2013.

S.H. Strogatz, Nonlinear Dynamics and Chaos with Application to Physics, Biology, Chemistry, and Engineering, Massachusets (US): Addison-Wesley Publishing Company, 1994.

J.K. Hale, and H. Kocak, Dynamic and Bifurcation, New York: Springer-Verlag, 1991.

H. Anton, and C. Rorres, Aljabar Linear Elementer, Jakarta: Erlangga, 1987.

M. Diska, Analisis Kestabilan Model Mangsa-Pemangsa Dengan Struktur Umur Pemangsa dan Fungsi Respon Monod-Haldane, Institut Pertanian Bogor, 2018.




DOI: https://doi.org/10.34312/euler.v8i2.10407

Refbacks

  • There are currently no refbacks.


Copyright (c) 2020 Muhammad Bachtiar Gaib, Wahdania At. Ja'a

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi has been indexed by:

                         EDITORIAL OFFICE OF EULER : JURNAL ILMIAH MATEMATIKA, SAINS, DAN TEKNOLOGI

 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Tilongkabila, Kabupaten Bone Bolango 96554, Gorontalo, Indonesia
 Email: euler@ung.ac.id
 +6287743200854 (Call/SMS/WA)
 Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi (p-ISSN: 2087-9393 | e-ISSN:2776-3706) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.  Powered by Public Knowledge Project OJS.