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Stability Analysis And Maximum Profit Of Logistic Population Model With Time Delay And Constant Effort Of Harvesting

Jurnal Matematika, Statistika dan Komputasi · Vol. 3 No. 1 (2018) · pp. 9–18

DOI
10.20956/jmsk.v3i1.3296
ISSN
2614-8811, 1858-1382
Published
2018-01-29
Publisher
Department of Mathematics, Hasanuddin University
Language
en

Abstract

In this paper we develop the logistic population model by considering a time delay and constant effort of harvesting. The time delay makes the model more accurate and harvesting is incorporated since the population is beneficial or the population is under control. We study the sufficient conditions to assure the existence of the population. Perturbation method is used to linearize the model and the stability of the equilibrium point is determined by inspection of the eigenvalues. The results show that there exists a globally asymptotically stable equilibrium point for the model with and without time delay and harvesting. The time delay can induce instability and a Hopf bifurcation can occur. The stable equilibrium point for the model with harvesting is then related to profit function problem. We found that there exists a critical value of the effort that maximizes the profit and the equilibrium point also remains stable. This means that the population can exist and give maximum profit although it is harvested with constant effort of harvesting.

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 And Maximum Profit Of Logistic Population Model With Time Delay And Constant Effort Of Harvesting</dc:title>
	<dc:creator xml:lang="en">Toaha, Syamsuddin</dc:creator>
	<dc:description xml:lang="en">In this paper we develop the logistic population model by considering a time delay and constant effort of harvesting. The time delay makes the model more accurate and harvesting is incorporated since the population is beneficial or the population is under control. We study the sufficient conditions to assure the existence of the population. Perturbation method is used to linearize the model and the stability of the equilibrium point is determined by inspection of the eigenvalues. The results show that there exists a globally asymptotically stable equilibrium point for the model with and without time delay and harvesting. The time delay can induce instability and a Hopf bifurcation can occur. The stable equilibrium point for the model with harvesting is then related to profit function problem. We found that there exists a critical value of the effort that maximizes the profit and the equilibrium point also remains stable. This means that the population can exist and give maximum profit although it is harvested with constant effort of harvesting.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2018-01-29</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
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	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/3296</dc:identifier>
	<dc:identifier>10.20956/jmsk.v3i1.3296</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 3 No. 1: July 2006; 9-18</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/3296/1833</dc:relation>
	<dc:relation>10.20956/j.v3i1.3296.g1833</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2018 Jurnal Matematika Statistika dan Komputasi</dc:rights>
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