Analisis kestabilan model mangsa-pemangsa Lotka-Volterra dengan mempertimbangkan waktu tunda = Stability analysis of Lotka-Volterra prey-predator model with time delay

Sitorus, Tasya Christie (2020) Analisis kestabilan model mangsa-pemangsa Lotka-Volterra dengan mempertimbangkan waktu tunda = Stability analysis of Lotka-Volterra prey-predator model with time delay. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Penelitian ini berfokus pada model interaksi mangsa-pemangsa Lotka-Volterra dengan mempertimbangkan waktu tunda. Penambahan waktu tunda membuat model klasik mangsa-pemangsa Lotka-Volterra menjadi lebih realistis. Tujuan penelitian ini untuk membangun model mangsa-pemangsa Lotka-Volterra dengan waktu tunda, menganalisa pengaruh waktu tunda pada model mangsa-pemangsa Lotka-Volterra, dan menentukan solusi numerik pada model mangsa-pemangsa Lotka-Volterra dengan waktu tunda. Metode yang dilakukan dalam penyelesaian penelitian ini adalah metode analitik dan metode numerik. Metode numerik dilakukan dengan menggunakan perangkat lunak MATLAB dan untuk mengimplementasikan permasalahannya menggunakan DDE23 (Delay Differential Equation 23). Analisa kestabilan dilakukan terhadap model mangsa-pemangsa Lotka-Volterra tanpa dan dengan waktu tunda. Hasil penelitian menunjukkan terdapat empat titik keseimbangan pada model mangsa-pemangsa Lotka-Volterra. Titik keseimbangan E0,E1, dan E2 tidak terpengaruh dengan waktu tunda. Sedangkan titik keseimbangan E3 terpengaruh oleh waktu tunda. Kestabilan pada titik keseimbangan E3 bergantung pada r2 dan besarnya waktu tunda r. Ada ambang batas waktu tunda r yang membuat titik keseimbangan E3 menjadi stabil dan tidak stabil. Titik keseimbangan E3 juga mempunyai hubungan dengan λ2 pada titik keseimbangan E1. Sedangkan hasil dari simulasi numerik pada penelitian ini, memperlihatkan kestabilan jumlah populasi mangsa dan pemangsa terhadap waktu t dan trayektori populasi mangsa dan pemangsa untuk suatu interval waktu t pada model mangsa-pemangsa Lotka-Volterra. / This research discusses the Lotka-Volterra prey-predator interaction model by considering the time delay. The addition of time delay makes the classical model of Lotka-Volterra prey more realistic. The purpose of this research is to investigate a Lotka-Volterra prey-predator model with a time delay, analyze the effect of the time delay on the Lotka-Volterra predator model, and determine the numerical solution in the Lotka-Volterra prey-predator model with a time delay. The methods used in the completion of this research are the analytical method and numerical method. The DDE23 (Delay Differential Equation 23) procedure built in MATLAB software is used to analyze the model numerically. Stability analysis was carried out on the Lotka-Volterra prey-predator model without and with a time delay. The results showed that there were four equilibrium points in the Lotka-Volterra prey-predator model. The equilibrium points of E0,E1, and E2 are not affected by the time delay. While the equilibrium point E3 is affected by the time delay. The stability at the equilibrium point E3 depends on r2 and the amount of delay r. There is a time delay r that makes the equilibrium point E3 stable and unstable. The equilibrium point E3 also has a relationship with λ2 at the equilibrium point E1. Whereas the results of numerical simulation in this research shows the stability of the number of prey and predator populations over the time of t and the trajectory of prey and predator populations for a time interval t in the Lotka-Volterra prey-predator model.

Item Type: Thesis (Bachelor)
Creators:
CreatorsNIMEmail
Sitorus, Tasya ChristieNIM00000020829tasyacsitorus@gmail.com
Contributors:
ContributionContributorsNIDN/NIDKEmail
Thesis advisorSaputra, Kie Van IvankyNIDN0401038203kie.saputra@uph.edu
Thesis advisorCahyadi, LinaNIDN0328077701lina.cahyadi@uph.edu
Uncontrolled Keywords: Lotka-Volterra; kestabilan; waktu tunda; titik keseimbangan
Subjects: Q Science > QA Mathematics
Divisions: University Subject > Current > Faculty/School - UPH Karawaci > Faculty of Science and Technology > Mathematics
Current > Faculty/School - UPH Karawaci > Faculty of Science and Technology > Mathematics
Depositing User: Users 5710 not found.
Date Deposited: 16 Jul 2020 02:17
Last Modified: 16 Jul 2020 02:17
URI: http://repository.uph.edu/id/eprint/9293

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