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Analisis Kestabilan Model Mangsa Pemangsa dengan Pemanenan Ambang Batas pada Populasi Pemangsa

Jurnal Matematika, Statistika dan Komputasi · Vol. 16 No. 1 (2019) · pp. 97–106

DOI
10.20956/jmsk.v16i1.6575
ISSN
2614-8811, 1858-1382
Published
2019-06-27
Publisher
Department of Mathematics, Hasanuddin University
Language
en

Abstract

Abstrak Penelitian ini mengkaji model satu mangsa dan satu pemangsa yang saling berkompetisi. Fungsi predasi dari pemangsa diasumsikan menggunakan fungs1 respon Holling tipe II. Dengan asumsi bahwa adanya kompetisi intraspesifik pada popuasi pemangsa serta dilakukan pemanenan ambang batas pada popuasi pemangsa. Pada model tersebut dilakukan analisis tentang syarat kewujudan dan kestabilan titik keseimbangan interior. Analisis kestabilan titik keseimbangan interior dilakukan dengan metode linearisasi dan dengan memperhatikan nilai eigen dari matriks Jacobi yang diperoleh. Terdapat sepuluh titik kesetimbangan yang diperoleh pada model, satu diantaranya dapat dinterpretasikan. Titik tersebut dinyatakan stabil asimtotik. Berdasarkan hasil anasis menggunakan beberapa parameter, diketahui bahwa ada suatu waktu pemanenan ambang batas harus dihentikan karna sudah tidak memenuhi syarat kriteria ambang batas yang telah ditentukan.Kata kunci: Model mangsa pemangsa, Pemanenan ambang batas, Titik kesetimbanganAbstract This study examines the model of one prey and one predator who mutates each other. The predation function of predators is assumed to use the Holling type II response function. Assuming that the existence of intraspecific competition in predatory population and theshold harvesting for predatory population is carried out. In this model, an analysis of the actual conditions and stability of the interior balance point is carried out. Analysis of the interior stability balance points was carried out by linearization method and by taking into account the eigenvalues of the Jacobian matrix obtained. There are ten equilibrium points of engagement obtained on the model, one of which can be interpreted. This point is stated as asymptotically stable. Based on the results of analysis using several parameters, it is known that there is a time when harvesting the threshold must be stopped because it has not fulfill the specified criteria for threshold.Keyword: Prey-predator model threshold harvesting, equibrium point

Keywords

Collaboration network of the authors

31 authors · 61 co-authorship links

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  • State University of Makassar
  • Affiliation unknown
  • Different organisations
  • Same organisation
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Co-authorOrganisationJoint articles
Khaeruddin KhaeruddinState University of Makassar3
Sulma SulmaAffiliation unknown3
Jeffry KusumaAffiliation unknown2
Syamsul AgusAffiliation unknown2
Himmatul Ulya FebriyantiAffiliation unknown2
Lilis Dwi Sapta AprilyaniAffiliation unknown2
Suriani SurianiAffiliation unknown2
Syamsir MuarafAffiliation unknown2
Nita AnggrianiAffiliation unknown2
Andi Utari SamsirAffiliation unknown2
Mutmainnah SyamsulAffiliation unknown2
Rabiatul AdawiyahAffiliation unknown2
I Nyoman WidanaAffiliation unknown1
Ita FitriaAffiliation unknown1
Sulfayanti SulfayantiAffiliation unknown1
Mawardi BahriAffiliation unknown1
IIN SUTRISNAAffiliation unknown1
Asriadi NasrunAffiliation unknown1
A. Muh. Amil SiddikAffiliation unknown1
Andi Muhammad AnwarAffiliation unknown1
Nur Suci RamadhaniAffiliation unknown1
Toaha ToahaAffiliation unknown1
Hukmah HukmahAffiliation unknown1
Ismi Ra'yan SyarifAffiliation unknown1
Sitti SahrimanAffiliation unknown1
Anisa KalondengAffiliation unknown1
M. Zaky Hisyam GozhiAffiliation unknown1
Aidul Fitri MustaminAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Analisis Kestabilan Model Mangsa Pemangsa dengan Pemanenan Ambang Batas pada Populasi Pemangsa</dc:title>
	<dc:creator xml:lang="en">Yusrianto, Yusrianto</dc:creator>
	<dc:creator xml:lang="en">Toaha, Syamsuddin</dc:creator>
	<dc:creator xml:lang="en">Kasbawati, Kasbawati</dc:creator>
	<dc:subject xml:lang="en">Prey-predator model threshold harvesting</dc:subject>
	<dc:subject xml:lang="en">equibrium point</dc:subject>
	<dc:description xml:lang="en">                                                                                        Abstrak Penelitian ini mengkaji model satu mangsa dan satu pemangsa yang saling berkompetisi. Fungsi predasi dari pemangsa diasumsikan menggunakan fungs1 respon Holling tipe II. Dengan asumsi bahwa adanya kompetisi intraspesifik pada popuasi pemangsa serta dilakukan pemanenan ambang batas pada popuasi pemangsa. Pada model tersebut dilakukan analisis tentang syarat kewujudan dan kestabilan titik keseimbangan interior. Analisis kestabilan titik keseimbangan interior dilakukan dengan metode linearisasi dan dengan memperhatikan nilai eigen dari matriks Jacobi yang diperoleh. Terdapat sepuluh titik kesetimbangan yang diperoleh pada model, satu diantaranya dapat dinterpretasikan. Titik tersebut dinyatakan stabil asimtotik. Berdasarkan hasil anasis menggunakan beberapa parameter, diketahui bahwa ada suatu waktu pemanenan ambang batas harus dihentikan karna sudah tidak memenuhi syarat kriteria ambang batas yang telah ditentukan.Kata kunci : Model mangsa pemangsa, Pemanenan ambang batas, Titik kesetimbanganAbstract This study examines the model of one prey and one predator who mutates each other. The predation function of predators is assumed to use the Holling type II response function. Assuming that the existence of intraspecific competition in predatory population and theshold harvesting for predatory population is carried out. In this model, an analysis of the actual conditions and stability of the interior balance point is carried out. Analysis of the interior stability balance points was carried out by linearization method and by taking into account the eigenvalues of the Jacobian matrix obtained. There are ten equilibrium points of engagement obtained on the model, one of which can be interpreted. This point is stated as asymptotically stable. Based on the results of analysis using several parameters, it is known that there is a time when harvesting the threshold must be stopped because it has not fulfill the specified criteria for threshold.Keyword : Prey-predator model threshold harvesting, equibrium point</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2019-06-27</dc:date>
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	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/6575</dc:identifier>
	<dc:identifier>10.20956/jmsk.v16i1.6575</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 16 No. 1 (2019): JMSK, July, 2019; 97-106</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/6575/3718</dc:relation>
	<dc:relation>10.20956/j.v16i1.6575.g3718</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2019 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
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