Aristya, Setya Dwi Yuli (2018) Analisis Dinamik Model Predator-Prey Dengan Struktur Usia Dan Fungsi Respon Tipe Monod-Haldane. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini dibahas suatu model predator-prey dengan struktur usia dan fungsi respon tipe Monod-Haldane. Model terdiri dari tiga variabel, yaitu x; y; dan z yang masing-masing menyatakan kepadatan populasi prey, predator remaja, dan predator dewasa. Pada model tersebut dilakukan analisis dinamik yang meliputi penentuan titik kesetimbangan dan analisis kestabilan lokal titik kesetimbangan. Hasil analisis dinamik menunjukkan bahwa model memiliki tiga titik kesetimbangan, yaitu titik kesetimbangaan trivial, titik kesetimbangan aksial, dan titik kesetimbangan interior. Titik kesetimbangan trivial dan aksial selalu eksis, sedangkan titik kesetimbangan interior eksis jika memenuhi syarat tertentu. Titik kesetimbangan trivial bersifat tidak stabil, sedangkan titik kesetimbangan aksial dan interior bersifat stabil asimtotik lokal jika memenuhi syarat tertentu. Hasil simulasi numerik mendukung hasil analisis dinamik yang diperoleh.
English Abstract
This final project discusses a model of stage structured predator-prey with Monod-Haldane type response function. The model consists of three variables, namely x; y; and z that represent population density of prey, juvenile predator, and adult predator, respectively. Dynamical analysis on the model includes determination of equilibrium point and local stability analysis of equilibrium point. The result of dynamical analysis shows that the model has three equilibrium points, namely trivial, axial, and interior point. The trivial and axial equilibrium points always exist, while the interior point exist under a certain condition. The trivial equilibrium point is unstable, while the axial and interior equilibrium points are local asymptotically stable under some conditions. The result of numerical simulation support the result of the dynamical analysis that have been obtained.
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2018/367/051807420 |
| Uncontrolled Keywords: | predator-prey model, stage structured, Monod-Haldane type response function, equilibrium point, local stability |
| Subjects: | 500 Natural sciences and mathematics > 515 Analysis > 515.3 Differential calculus and equations |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Endang Susworini |
| Date Deposited: | 13 Jun 2020 01:00 |
| Last Modified: | 13 Jun 2020 01:00 |
| URI: | http://repository.ub.ac.id/id/eprint/168910 |
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