Adiningsih, Nur Evita (2018) Analisis dinamik sistem persamaan diferensial predator-prey tiga spesies. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.
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Abstract
INDONESIA:
Salah satu model interaksi antar makhluk hidup dalam suatu ekosistem adalah model predator-prey tiga spesies. Predator-prey tiga spesies ini tersusun dari satu spesies prey, satu spesies intermediate predator, dan satu spesies top predator. Prey merupakan spesies yang dimangsa oleh intermediate predator dan top predator. Intermediate predator merupakan spesies yang memangsa prey tetapi juga dimangsa oleh top predator. Sedangkan top predator adalah spesies yang memangsa prey dan intermediate predator. Model dari predator-prey tiga spesies ini berbentuk sistem persamaan diferensial nonlinier. Berdasarkan permasalahan di atas maka penelitian ini bertujuan untuk mengetahui bagaimana analisis dinamik dari model predator-prey tiga spesies tersebut. Sehingga diharapkan dapat mengetahui bagaimana arah kepunahan suatu spesies predator maupun prey. Hasil analisis dinamik dari sistem persamaan diferensial predator-prey tiga spesies didapatkan tiga titik tetap yaitu titik tetap (a) x_1=1,y_1=0, dan z_1=0 (tidak stabil), (b) x_2=0,3297008434,〖 y〗_2= 2,486229719, dan z_2=0 (tidak stabil), (c)x_3=0,2445212315,y_3=0,08667445145, dan z_3= 0,4485840923 (tidak stabil).
ENGLISH:
One model of interaction between living things in an ecosystem is a predator-prey of three species model. The predator-prey of three species is composed of one species of prey, one species of intermediate predator, and one species of predator. Preys are species that is preyed by intermediate predators and top predators. Intermediate predators are species that prey on preys but are also preyed by top predators. While top predators are species that prey on preys and intermediate predators. The model of the predator-prey of these three species is a system of nonlinier differential equations. Based on the problem then this research is aimed to know how dynamic analysis from predator-prey of three species model. So it is expected to know how the extinction of the predator or the prey. The results of this study indicate that (a) x_1=1,y_1=0,and z_1=0(unstable), (b) x_2=0,3297008434,〖 y〗_2= 2,486229719, and z_2=0(unstable), (c)x_3=0,2445212315,y_3=0,08667445145, and z_3= 0,4485840923 (unstable).
| Item Type: | Thesis (Undergraduate) | |||||||||
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| Supervisor: | Pagalay, Usman and Abdussakir, Abdussakir | |||||||||
| Contributors: |
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| Keywords: | Predator-Prey Tiga Spesies; Rantai Makanan; Ekosistem; Kestabilan; Analisis dinamik; Model populasi; Predator-Prey Three Species; Food Chain; Ecosystem; Stability; Dynamic Analysis; Population Model | |||||||||
| Departement: | Fakultas Sains dan Teknologi > Jurusan Matematika | |||||||||
| Depositing User: | Heni Kurnia Ningsih | |||||||||
| Date Deposited: | 04 Mar 2019 17:15 | |||||||||
| Last Modified: | 04 Mar 2019 17:15 | |||||||||
| URI: | http://etheses.uin-malang.ac.id/id/eprint/13312 |
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