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ITS » Undergraduate Theses » Matematika
Posted by budi at 06/01/2010 09:55:36  •  4367 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.

Keywordskemostat; mangsa-pemangsa; stabilitas
 
Subject:  Persamaan diferensial
Alt. Subject: Differential equations
Contributor
  1. 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

Coverage
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Rights
Copyright @2009 by ITS Library. This publication is protected by copyright and per obtained from the ITS Library prior to any prohibited reproduction, storage in a re transmission in any form or by any means, electronic, mechanical, photocopying, reco For information regarding permission(s), write to ITS Library


Publication URL :
http://digilib.its.ac.id/analisa-stabilitas-model-predatorprey-di-dalam-kemostat-dengan-fungsi-respon-umum-6926.html




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  1.  ITS-Undergraduate-6926-1200109017-Abstract.pdf - 61 KB
  2.  ITS-Undergraduate-6926-1200109017-kesimpulan.pdf - 15 KB

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