Analisis p-bifurkasi pada model stokastik Verhulst = P-bifurcation analysis on stochastic Verhulst model

Emilio, Joey (2022) Analisis p-bifurkasi pada model stokastik Verhulst = P-bifurcation analysis on stochastic Verhulst model. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Dalam Skripsi ini, akan dibahas dinamika solusi dari suatu model populasi yang bersifat stokastik. Salah satu manfaat dari penelitian ini adalah untuk mencegah kepunahan. Analisis dinamika solusi dapat dilakukan dengan mencari bifurkasi pada model tersebut. Kegunaan dari mencari bifurkasi pada model adalah klasifikasi parameter agar dapat melihat perilaku pada sebuah sistem jangka panjang. Dalam penelitian ini, akan dianalisis salah satu model populasi, yaitu model Verhulst. Lalu, akan ditentukan sifat bifurkasi pada model Verhulst dan nilai parameter yang dapat menyebabkan kepunahan dari suatu populasi. Terdapat dua titik bifurkasi stokastik pada model Verhulst yang ditentukan melalui dua metode yang berbeda. Metode pertama adalah dengan melakukan pengecekan pada nilai deterministik. Nilai determinsitik akan diperiksa apakah masuk ke dalam selang kepercayaan dari data solusi model stokastik pada t = 100. Melalui metode pertama, didapatkan bahwa dugaan titik bifurkasi pada saat 0,08 ≤ λ ≤ 0, 09. Metode kedua adalah dengan menganalisis p-value dari solusi X(t) di t = 1,2,3,..., 100. Melalui metode kedua, didapatkan bahwa titik bifurkasi pada saat 0,2 ≤ λ ≤ 0, 21. Berdasarkan analisis grafik rata-rata solusi X(t), ada kemungkinan populasi akan punah pada λ = 0,8. / This Thesis will discussed the solution dynamics of a stochastic population model. One of the benefits of this research is to prevent the extinction. Solution dynamics analysis can be done by finding the bifurcation of the model. The use of finding the bifurcation of the model is classification of parameters in order to be able to see the behavior of a system in the long run. This research was made to analyze one of population model, that is Verhulst model. Then, bifurcation characteristic and parameter value which can cause a population to extinct will be determined. There are two point of stochastic bifurcation on Verhulst model that are determined through two methods. The first method is by checking on deterministic value. The deterministic value will be checked whether it goes into the confidence interval of the stochastic model solutions data at X(100). Through the first method, the bifurcation point is suspected in 0,08 ≤ λ ≤ 0, 09. The second method is by analyze p-value of the solution X(t) at t = 1,2,3,...,100. Through the second method, the bifurcation point is suspected in 0,2 ≤ λ ≤ 0,21. Based on the average graphical analysis of X(t), there is a possibility the population will become extinct at λ = 0,8.

Item Type: Thesis (Bachelor)
Creators:
CreatorsNIMEmail
Emilio, JoeyNIM01112180022joeyemilio00@gmail.com
Contributors:
ContributionContributorsNIDN/NIDKEmail
Thesis advisorSaputra, Kie Van IvankyNIDN0401038203kie.saputra@uph.edu
Thesis advisorCahyadi, LinaNIDN0328077701lina.cahyadi@uph.edu
Uncontrolled Keywords: Model Verhulst; Persamaan diferensial stokastik; Bifurkasi stokastik; Simulasi; Metode numerik
Subjects: Q Science > QA Mathematics
Divisions: University Subject > Current > Faculty/School - UPH Karawaci > Faculty of Science and Technology > Mathematics
Current > Faculty/School - UPH Karawaci > Faculty of Science and Technology > Mathematics
Depositing User: Users 6043 not found.
Date Deposited: 22 Feb 2022 02:13
Last Modified: 22 Feb 2022 02:13
URI: http://repository.uph.edu/id/eprint/46535

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