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Stability Analysis of Wangersky-Cunningham Model with Constant Effort of Harvesting

Jurnal Matematika, Statistika dan Komputasi · Vol. 12 No. 2 (2018) · pp. 140–152

DOI
10.20956/jmsk.v12i2.3469
ISSN
2614-8811, 1858-1382
Published
2018-02-04
Publisher
Department of Mathematics, Hasanuddin University
Language
en

Abstract

In this paper we consider another predator-prey model with time delay which is called the Wangersky-Cunningham model. In this model, the rate of change of the predator population depends on the numbers of prey and predator present at some previous time. The model is then improved by considering a constant effort of harvesting into the growth rate of the prey and predator populations. The method use in this analysis is linearization the model around the equilibrium point and then inspecting the eigenvalues to determine the stability. We found that there exists a positive equilibrium point for the model with and without harvesting. The time delay can induce instability and Hopf bifurcation can also occur. Some plots of trajectories of the prey and predator populations are also given.

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
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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 Wangersky-Cunningham Model with Constant Effort of Harvesting</dc:title>
	<dc:creator xml:lang="en">Toaha, Syamsuddin</dc:creator>
	<dc:description xml:lang="en">In this paper we consider another predator-prey model with time delay which is called the Wangersky-Cunningham model. In this model, the rate of change of the predator population depends on the numbers of prey and predator present at some previous time. The model is then improved by considering a constant effort of harvesting into the growth rate of the prey and predator populations. The method use in this analysis is linearization the model around the equilibrium point and then inspecting the eigenvalues to determine the stability. We found that there exists a positive equilibrium point for the model with and without harvesting. The time delay can induce instability and Hopf bifurcation can also occur. Some plots of trajectories of the prey and predator populations are also given.</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/3469</dc:identifier>
	<dc:identifier>10.20956/jmsk.v12i2.3469</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 12 No. 2: January 2016; 140-152</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/3469/1998</dc:relation>
	<dc:relation>10.20956/j.v12i2.3469.g1998</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2018 Syamsuddin Toaha</dc:rights>
</oai_dc:dc>