Rayungsari, Maya (2013) Analisis Dinamik Model Predator-Prey dengan Fungsi Respon Ratio-Dependent dan Pemanenan pada Predator. Magister thesis, Universitas Brawijaya.
Abstract
Pada tesis ini dibahas konstruksi dan analisis model predator-prey dengan fungsi respon ratio-dependent dan pemanenan pada predator . Model tersebut merupakan sistem persamaan diferensial biasa nonlinear dengan dua variabel, yaitu kepadatan populasi prey ( N ) dan kepadatan populasi predator ( P ). Berdasarkan hasil analisis, sistem memiliki tiga titik kesetimbangan, yaitu titik kepunahan prey , titik kepunahan predator , dan titik koeksistensi. Sifat kestabilan lokal ketiga titik kesetimbangan tersebut ditentukan dengan cara melinearkan sistem di sekitar titik kesetimbangan dan memeriksa tanda nilai eigen matriks Jacobi sistem di setiap titik kesetimbangan. Titik kepunahan predator bersifat tidak stabil, sementara titik kepunahan prey dan titik koeksistensi stabil asimtotik lokal dengan syarat tertentu. Untuk mengilustrasikan kestabilan kedua titik kesetimbangan tersebut, dilakukan simulasi numerik menggunakan metode Runge Kutta orde empat dengan bantuan software Matlab. Diperoleh bahwa hasil numerik sesuai dengan hasil analitik. Melalui simulasi numerik juga diperoleh pengaruh pemanenan predator terhadap sistem, yaitu mengubah jumlah predator yang dapat bertahan hidup dan mencegah kepunahan prey .
English Abstract
In this thesis, construction and analysis of predator-prey model with ratiodependent functional response and predator harvesting are discussed. The model is a nonlinear ordinary differential equation system with two variables, namely prey density ( N ) and predator density ( P ). According to the analysis, three equilibrium points are obtained, namely the prey extinction, the predator extinction, and coexistence point. Local stability properties of these equilibrium points are determinated by linearyzing the system around each equilibrium points and evaluating the sign of all eigenvalues of the Jacobian matrix of the system at each equilibrium point. The predator extinction point is unstable, while the prey extinction and coexistence point are local asymtotically stable under certain conditions. To give some illustrations about the stability of both equilibrium points. numerical simulations are performed by using fourth-order Runge Kutta method with the help of Matlab software. It is found that numerical results coincide with analytical result. From numerical simulations, the effects of predator harvesting to the system are obtained, those are changing the amount of predator that can survive and preventing prey extinction.
| Item Type: | Thesis (Magister) |
|---|---|
| Identification Number: | TES/515.39/RAY/a/041307548 |
| Subjects: | 500 Natural sciences and mathematics > 515 Analysis > 515.3 Differential calculus and equations |
| Divisions: | S2/S3 > Magister Matematika, Fakultas MIPA |
| Depositing User: | Endro Setyobudi |
| Date Deposited: | 24 Jan 2014 10:54 |
| Last Modified: | 24 Jan 2014 10:54 |
| URI: | http://repository.ub.ac.id/id/eprint/157453 |
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