Huda, Moh. Nurul (2017) Analisis Dinamik Model Rantai Makanan Hastings-Powell Orde Fraksional Dengan Makanan Tambahan. Magister thesis, Universitas Brawijaya.
Abstract
Tesis ini membahas model rantai makanan Hasting-Powell orde fraksional dengan makanan tambahan. Model dikonstruksi dengan menggunakan orde fraksional karena mempertimbangkan efek memori. Oleh sebab itu, laju perubahan populasi prey dan predator tidak hanya bergantung pada keadaan saat ini melainkan semua keadaan sebelumnya. Pembahasan tentang analisis dinamik pada model orde fraksional meliputi penentuan titik kesetimbangan, syarat eksistensi dan kestabilannya. Berdasarkan hasil analisis diperoleh empat titik kesetimbangan yang eksis, yaitu titik kepunahan ketiga populasi ( ), kepunahan populasi intermediate-predator dan top-predator ( ), kepunahan populasi top-predator ( ), dan ketiga populasi mampu bertahan hidup ( ). Titik kesetimbangan bersifat tidak stabil dan titik kesetimbangan , , dan bersifat stabil lokal dengan syarat. Hasil simulasi numerik dengan pendekatan Grunwald-Letnikov menunjukkan hasil yang sesuai dengan hasil secara analisis.
English Abstract
This thesis discusses a fractional-order Hastings-Powell food chain model with additional food. The model is constructed using fractional order to include the memory effect. Therefore, the rate of both prey and predator population depend not only on the current state but also all the previous state. The discussion of dynamical analysis on the fractional order model includes the determination of equilibrium points, existence conditions and their stability. There are four equilibrium points that exist, namely the extinction point of all population ( ), the extinction point of intermediate-predator and top-predator populations ( ), the extinction point of the top-predator populations ( ), and the point of three populations can survive ( ). The equilibrium point of is unstable and the others are locally asymptotically stable with some conditions. The result of numerical simulation is derived using Grunwald-Letnikov approach. It can be shown that the results of numerical simulations are in accordance with analytical results.
| Item Type: | Thesis (Magister) |
|---|---|
| Identification Number: | TES/519.5/HUD/a/2017/041709422 |
| Uncontrolled Keywords: | FOOD CHAINS (ecology) - MATHEMATICAL MODELS, PREDATION (biology), PREDATION (biology) - MATHEMATICAL BIOLOGY, FRACTIONAL CALCULUS |
| Subjects: | 500 Natural sciences and mathematics > 519 Probabilities and applied mathematics > 519.5 Statistical mathematics |
| Divisions: | S2/S3 > Magister Matematika, Fakultas MIPA |
| Depositing User: | Nur Cholis |
| Date Deposited: | 10 Nov 2017 07:13 |
| Last Modified: | 29 Nov 2021 02:25 |
| URI: | http://repository.ub.ac.id/id/eprint/5273 |
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