Putra, M. Adib Jauhari Dwi (2017) Analisis Kestabilan Dan Bifurkasi Hopf Model Predator-Prey Pada Kasus Intraguild Predation Dengan Fungsi Respon Holling Tipe Ii. Magister thesis, Universitas Brawijaya.
Abstract
Pada tesis ini dikaji suatu model predator-prey yang menggambarkan intraguild predation dengan fungsi respon Holling tipe II. Carrying capacity predator dan prey bergantung pada kepadatan populasi sumber biotik yang berubah terhadap waktu. Analisis dinamik model meliputi penentuan titik kesetimbangan, eksistensi, kestabilan lokal titik kesetimbangan dan bifurkasi Hopf. Diperoleh tiga jenis titik kesetimbangan, yaitu titik kepunahan prey dan titik kepunahan predator yang selalu eksis, serta titik kesetimbangan interior yang eksis dengan kondisi tertentu. Titik kepunahan predator selalu bersifat tidak stabil, sedangkan titik kepunahan prey dan titik kesetimbangan interior bersifat stabil asimtotik dengan kondisi tertentu. Terdapat kemungkinan sistem dengan dua titik kesetimbangan yang stabil atau disebut sistem bistabil. Sistem bistabil mengindikasikan bahwa kestabilan sistem bergantung pada nilai awal ketiga populasi. Bifurkasi Hopf terjadi di sekitar titik kesetimbangan interior. Simulasi numerik dilakukan untuk mengkonfirmasi hasil analisis.
English Abstract
This thesis concerns with a predator-prey model describing intraguild predation with Holling type II functional response. Carrying capacity of the predator and prey depend on the number of biotic resources that varies in time. Mathematical analysis of the model includes the existence and local stability of equilibrium points as well as Hopf bifurcation. Three kinds of equilibrium points have been found, namely the extinction of prey point, the extinction of predator point and the interior equilibrium point. The extinction of prey point and the extinction of predator point always exist, while the interior equilibrium may exist under certain conditions. The extinction of predator point is always unstable. The extinction of prey point and the interior equilibrium point are conditionally asymptotically stable. There is possibility system with two stable equilibiriums which called as bistable system. Bistable system indicates that stability of the system is depending on initial values of the populations. Hopf bifurcation occurs around the interior equilibirium point. Numerical simulations are performed to confirms the analytical results.
| Item Type: | Thesis (Magister) |
|---|---|
| Identification Number: | TES/591.53/PUT/a/2017/041705302 |
| Uncontrolled Keywords: | DIFERENTIAL EQUATIONS, NONLINEAR, HOPF ALGEBRAS |
| Subjects: | 500 Natural sciences and mathematics > 515 Analysis > 515.3 Differential calculus and equations > 515.35 Differential equations |
| Divisions: | S2/S3 > Magister Matematika, Fakultas MIPA |
| Depositing User: | Nur Cholis |
| Date Deposited: | 21 Jul 2017 02:55 |
| Last Modified: | 18 Dec 2020 00:54 |
| URI: | http://repository.ub.ac.id/id/eprint/467 |
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