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Stability Analysis of Prey-Predator Population Model with Harvesting on The Predator Population

Jurnal Matematika, Statistika dan Komputasi · Vol. 12 No. 1 (2018) · pp. 48–59

DOI
10.20956/jmsk.v12i1.3457
ISSN
2614-8811, 1858-1382
Published
2018-02-04
Publisher
Department of Mathematics, Hasanuddin University
Language
en

Abstract

In this paper we present a deterministic and continuous model for one prey–one predator population model based on Lotka-Volterra model. The predator population is subjected to both constant effort and constant quota of harvesting. We study analytically the sufficient conditions of harvesting to ensure the stability of the equilibrium point. The method used to analyze the stability of the equilibrium point is linearization and Hurwitz stability test. The results show that the equilibrium point which occurs in positive quadrant is stable although the predator population is subjected to harvesting. This means that the prey and predator populations can live in coexistence although the predator is harvested provided the level of harvesting is controlled. Some examples are given to illustrate the behavior of the trajectories.

Collaboration network of the authors

29 authors · 58 co-authorship links

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  • State University of Makassar
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Kasbawati KasbawatiAffiliation unknown12
Khaeruddin KhaeruddinState University of Makassar3
Sulma SulmaAffiliation unknown2
Jeffry KusumaAffiliation unknown2
I Nyoman WidanaAffiliation unknown1
Ita FitriaAffiliation unknown1
Sulfayanti SulfayantiAffiliation unknown1
Syamsul AgusAffiliation unknown1
Mawardi BahriAffiliation unknown1
IIN SUTRISNAAffiliation unknown1
Asriadi NasrunAffiliation unknown1
Yusrianto YusriantoAffiliation unknown1
Himmatul Ulya FebriyantiAffiliation unknown1
Lilis Dwi Sapta AprilyaniAffiliation unknown1
Suriani SurianiAffiliation unknown1
A. Muh. Amil SiddikAffiliation unknown1
Andi Muhammad AnwarAffiliation unknown1
Syamsir MuarafAffiliation unknown1
Nita AnggrianiAffiliation unknown1
Andi Utari SamsirAffiliation unknown1
Hukmah HukmahAffiliation unknown1
Ismi Ra'yan SyarifAffiliation unknown1
Mutmainnah SyamsulAffiliation unknown1
Rabiatul AdawiyahAffiliation 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">Stability Analysis of Prey-Predator Population Model with Harvesting on The Predator Population</dc:title>
	<dc:creator xml:lang="en">Toaha, Syamsuddin</dc:creator>
	<dc:description xml:lang="en">In this paper we present a deterministic and continuous model for one prey–one predator population model based on Lotka-Volterra model. The predator population is subjected to both constant effort and constant quota of harvesting. We study analytically the sufficient conditions of harvesting to ensure the stability of the equilibrium point. The method used to analyze the stability of the equilibrium point is linearization and Hurwitz stability test. The results show that the equilibrium point which occurs in positive quadrant is stable although the predator population is subjected to harvesting. This means that the prey and predator populations can live in coexistence although the predator is harvested provided the level of harvesting is controlled. Some examples are given to illustrate the behavior of the trajectories.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2018-02-04</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/3457</dc:identifier>
	<dc:identifier>10.20956/jmsk.v12i1.3457</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 12 No. 1: July 2015; 48-59</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/3457/1988</dc:relation>
	<dc:relation>10.20956/j.v12i1.3457.g1988</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2018 Syamsuddin Toaha</dc:rights>
</oai_dc:dc>