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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.

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Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 8 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>
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