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ITS » Undergraduate Theses » Matematika Posted by budi at 06/01/2010 09:55:36 • 4961 Views
ANALISA STABILITAS MODEL PREDATOR-PREY DI DALAM KEMOSTAT DENGAN FUNGSI RESPON UMUM
STABILITY ANALYSIS OF PREDATOR-PREY MODEL IN A CHEMOSTAT WITH GENERAL RESPONSE FUNCTION
Author : WULANDHANI, NURLITA CATUR
ABSTRAK
Ruang pertumbuhan dalam kemostat memungkinkan terjadinya interaksi mangsa-pemangsa yang bisa dimodelkan secara matematis. Dengan adanya laju perpindahan dan fungsi respon dalam model matematis yang digambarkan maka mengakibatkan sistem tidak
konservatif tidak memenuhi hukum kekekalan energi. Sehingga untuk mengetahui stabilitas sistem dilakukan melalui dua tahapan yaitu stabilitas lokal terlebih dahulu kemudian stabilitas global. Dalam menganalisa stabilitas lokal digunakan kriteria Routh-Hurwitz dan stabilitas global dengan kondisi steady state yang bebas dari predator melalui konstruksi fungsi Liapunov. Analisa persistensi melengkapi analisa stabilitas yang dilakukan terhadap model interaksi mangsa pemangsa di dalam kemostat dengan fungsi respon umum sehingga bisa diidentifikasi kesetimbangan sistem dalam keadaan sebenarnya.
ABSTRACT
Growth medium in a chemostat enabling predator-prey interaction which can be modeled thematically. With a removal rates and response functions of used mathematical model it caused unconservative system. To know its stability hence divided on two
parts such as local stability then global stability. Local stability of steady states is studied by using Routh-Hurwitz criterion and used constructing of Lyapunov function in the study of global stability include predator-free steady state. Persistence analysis completed stability analysis of predator-prey model in a chemostat with general response functions so could identify system balancely state in fact.
Keywords:
kemostat; mangsa-pemangsa; stabilitas
Subject
: Persamaan diferensial
Contributor
Drs. M. SETIJO WINARKO, M. Si
Date Create
: 06/01/2010
Type
: Text
Format
: Pdf
Language
: Indonesian
Identifier
: ITS-Undergraduate-3100009036071
Collection ID
: 3100009036071
Call Number
: RSMa 515.35 Wul a
Source Undergraduate Theses, Mathematics,RSMa 515.35 Wul a, 2009
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