Artha, RizkiYuni (2013) Model Pertumbuhan Populasi Predator-Prey Dengan Efek Allee Dan Fungsi Respon Holling Tipe II. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini dibahas model predator-prey kontinu dengan efek Allee. Laju pertumbuhan prey mengikuti model logistik. Efek Allee pada model ini terjadi pada laju pertumbuhan populasi prey. Analisis dinamik model meliputi perhitungan titik kesetimbangan, syarat eksistensi titik kesetimbangan, analisis kestabilan lokal titik kesetimbangan dan kestabilan global titik kesetimbaangan. Pada bagian akhir dilakukan simulasi numerik dengan menggunakan metode Runge-Kutta orde empat untuk mengilustrasikan hasil analisis. Model dianalisis untuk memperoleh sifat kestabilan lokal titik kesetimbangan model. Selanjutnya, dari simulasi numerik tersebut ditemukan bahwa Allee yang bernilai besar akan menyebabkan populasi predator dan prey punah namun apabila Allee bernilai kecil maka populasi prey dan predator tidak akan punah.
English Abstract
This final project deals with continous predator prey model with Allee effect. It is assumed that growth rate of prey follows the logistic model. This Allee effect in the prey equation. Dynamical behaviour such as existence condition for each equilibrium point, local property as well as global property are addressed. Finally, numerical simulations are performed using fourth order Runge-Kutta to illustrate the analytical results. From numerical simulations it is found Allee that have big amount causes predator and prey population lose, but if Allee have small amount predator and prey population will never lose.
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2013/262/051307420 |
| Subjects: | 500 Natural sciences and mathematics > 510 Mathematics |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Hasbi |
| Date Deposited: | 04 Sep 2013 10:18 |
| Last Modified: | 25 Oct 2021 02:13 |
| URI: | http://repository.ub.ac.id/id/eprint/153519 |
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