Analysis of The Competition Model of Two Populations Around The Orbit of The Equilibrium Point
DOI:
10.56566/sigmamu.v2i2.283Downloads
Abstract
The competition of two populations model that represented in an ordinary differential equations system. This model describes about the competition of two population in general that is consist of the interspesies competition and the intraspesies competition. In ecology, the population dynamic is closely related to population growth, equilibrium, and stability. Equilibrium is represented by a point called the equilibrium point or fixed point. By analyzing the stability around the fixed point, it can be seen the carrying capacity of a system, which mean the optimal number of individual that can be supported by the environment. According to the analysis of the model obtained 4 fixed points, three of them are unstable and the other else is stable. The orbit of the system around fixed point visualized using software. The behavior orbit around fixed point of the model will move away from the unstable fixed point and move closer to the stable fixed point.
Keywords:
Equilibrium Orbit Competition of two population model Carrying capacity of a modelReferences
Anggriani, I., Nurhayati, S., & Subchan, S. (2018). Analisis Kestabilan Model Penurunan Sumber Daya Hutan Akibat Industri. Limits: Journal of Mathematics and Its Applications, 15(1), 31. https://doi.org/10.12962/limits.v15i1.3560
Asmaidi, T. S. A. (2021). Pemodelan Matematika Penyebaran COVID19 Tipe SV1V2EIR. Jurnal ASEECT, 2(2), 11–15.
Chauvet, E., Paullet, J. E., Previte, J. P. & Walls, Z. 2002. A Lotka-Volterra Three-Spescies Food Chain. Mathematics Magazine, 75 : 243 − 255.
Clarke, G. L. (1954). Elements of Ecology. Chapman & Hall.
D. K. Arrowsmith, C. M. P. (n.d.). Dynamical Systems: Differential Equations, Maps, and Chaotic Behaviour. Chapman & Hall, 1992.
Eka Nila Lospayadi Nurhamiyawan, Bayu Prihandono, H. (2013). Analisis Dinamika Model Kompetisi Dua Populasi Yang Hidup Bersama Di Titik Kesetimbangan Tidak Erdefinisi. Buletin Ilmiah Mat. Stat. Dan Terapannya (Bimaster), 02(3), 197 – 204
G. A. Ngwa and W. S. Shu. (2000). , “A mathematical model for endemic malaria with variable human and mosquito populations,” Math. Comput. Model., vol. 32, no. 7–8, 2000, doi: 10.1016/S0895- 7177(00)00169-2. Math. Comput. Model, 32(7–8).
Jumainisa, S., Darmawijoyo. & Hartono, Y. (2018). “Pengembangan Soal Mathematical Modelling Menggunakan Konteks Kesehatan Kelas V Sekolah Dasar”. Prosiding Seminar Nasional Stkip Pgri Sumatera Barat, 4(1).
Listyana, L. (2016). Analisis Bifurkasi pada Model Matematika Predator – Prey dengan Dua Predator. Universitas Negeri Yogyakarta.
Moneim, I. A., & Khalil, H. A. (2015). Modelling and Simulation of the Spread of HBV Disease with Infectious Latent. Applied Mathematics, 06(05), 745–753. https://doi.org/10.4236/am.2015.65070
Monica, Ritanica, dkk. (2014). Kestabilan Populasi Model Lotka – Volterra Tiga Spesies dengan Titik Keseimbangan. JOM FMIPA Volume 1 No. 2 Oktober 2014., 1(2).
Mu’tamar, K., dan Zulkarnain. (2017). Model Predator-Prey dengan Adanya Infeksidan Pengobatan pada Populasi Mangsa. Jurnal Sains, Teknologi dan Industri, 15(1), 1-6
Nurhamiyawan, E. N. L., Prihandono, B., & Helmi. (2018). Analisis Dinamika Model Kompetisi Dua Populasi yang Hidup Bersama di Titik Kesetimbangan Tidak Terdefinisi. Buletin Ilmiah Matematika Statistika Dan Terapannya, 02(3), 197–204.
Robinson, R.C. 2004. An Introduction to Dynamical Systems: Continuous and Discrete. Prenctice Hall, Reading, MA.
Rosyid, F. (2012). Analisis Kestabilan dan Limit Cycle pada Model Predator – Prey Tipe Gause. Skripsi.
Song, Y. dan Y. Peng, Stability and bifurcation analysis on a Logistic model with discrete and distributed delays, Applied Mathematics and Computations, 181, hal. 1745-1757, 2006
S. Side, W. Sanusi, and N. K. Rustan. (2020). “Model matematika SIR sebagai solusi kecanduan penggunaan media sosial,.” J. Math. Comput. Stat, 3(2), 126.
Sun, C.J., M.A. Han dan Y.P. Yang, Analysis of stability and Hopf bifurcation for a delayed logistic equation, Chaos, Soliton and Fractals, 31, hal. 672-682, 2007
Volterra Predator-Prey System. J. Comput. Appl. Math., vol.70: 658-670.
Zhao, H. dan Y.Lin. 2009. Hopf Bifurcation in A Partial Dependent Predator-Prey System with Delay. Chaos Solitons and Fractal, vol.42: 896-900.
Zhang, J., Z. Jin, J. Yan, dan G. Sun. 2009. Stability and Bifurcation Analysis for A Delayed Lotka
Zhang, F., Chen Y., dan Li J. (2018). Dynamical Analysis of a Stagestructured Predator-Prey Model with Cannibalism. Mathematical Biosciences, 307, 33-41
License
Copyright (c) 2024 Gilang Primajati, M. Gunawan Supiarmo, Agus Sofian Eka Hidayat
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
