Hidayatulloh, MuhammadRif`an (2013) Analisis Dinamik Model Rantai Makanan Lima Unsur Ekosistem Laut. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini dibahas model rantai makanan suatu ekosistem mikrobiologi di lautan, di mana terjadi proses makan-memakan antara spesies-spesies di dalamnya. Terdapat empat laju pertumbuhan populasi yang dikaji, yakni populasi bakteri, fitoplankton, zooplankton, dan protozoa, serta dipandang pula perubahan kepadatan unsur nutrisi. Kondisi tersebut menghasilkan suatu sistem persamaan diferensial lima dimensi. Untuk memudahkan analisis, dilakukan penskalaan terhadap model awal. Selanjutnya ditentukan titik kesetimbangan, syarat eksistensi titik kesetimbangan, dan kestabilan lokal titik kesetimbangan. Diperoleh delapan titik kesetimbangan, dua di antaranya memerlukan syarat eksistensi. Di antara delapan titik kesetimbangan tersebut, lima titik kesetimbangan stabil dengan syarat tertentu. Pada bagian akhir dilakukan simulasi numerik untuk mengilustrasikan dan menguji hasil analisis yang telah diperoleh.
English Abstract
This final project discuss a food chain model on a microbiology ecosystem in ocean, where predation process occur. Four population growth rates are discussed, namely bacteria, fitoplankton, zooplankton, and protozoa. The growths of nutrient density is also considered. These growths are governed by a five dimensional dynamical system. For sake of simplicity, the model is scalled. Dynamical behavior, such as existence condition for each equilibrium point, and thus local stabilities, are addressed. There are eight equilibrium points, where two of them exist maker certain conditions. Among the eight equilibriums, some equilibrium points are stable if the Ruth-Hurwitz criteria are satisfied. Finally, numerical simulation are carried out to ilustrate analytical findings.
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2013/339/051308470 |
| Subjects: | 500 Natural sciences and mathematics > 510 Mathematics |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Hasbi |
| Date Deposited: | 01 Oct 2013 10:34 |
| Last Modified: | 25 Oct 2021 02:25 |
| URI: | http://repository.ub.ac.id/id/eprint/153600 |
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2._Mukadimah.pdf Download (2MB) | Preview |
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3._Isi_(bab_1,2,3).pdf Download (2MB) | Preview |
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