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Dynamics Analysis of Predator-Prey Model with Double Allee Effects and Holling Type II Functional Response

Analisis Dinamik Model Mangsa Pemangsa dengan Efek Allee Ganda dan Fungsi Respon Holling Tipe II

Jurnal Matematika, Statistika dan Komputasi · Vol. 18 No. 3 (2022) · pp. 434–446

DOI
10.20956/j.v18i3.19237
ISSN
2614-8811, 1858-1382
Published
2022-05-15
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

In this article, a predator prey model with double Allee effects and Holling type II functional response is discussed. Strong and weak Allee effects were analyzed separately. The dynamic behavior of the model is analyzed by determining the equilibrium point and stability around the equilibrium point. From the analysis result, it is obtained that the trivial equilibrium point is locally asymptotically stable for the case of the strong Allee effect and the saddle unstable for the case of the weak Allee effect, while the boundary and coexistence equilibrium points are locally asymptotically stable if it satisfies several parameter conditions. Numerical simulations are carried out around the coexistence equilibrium point. The simulation results show that the Allee effect threshold affects prey population growth when experiencing a strong Allee effect. The growth of the prey population also depends on the initial conditions of the prey and predator population density. Furthermore, when the prey population experiences a weak Allee effect, there is no threshold must be exceeded for the population to survive so that for each initial condition however, the population will not experience extinction.

Bahasa Indonesia

Pada artikel ini dibahas model mangsa pemangsa dengan efek Allee ganda dan fungsi respon Holling tipe II. Efek Allee kuat dan lemah dianalisis secara terpisah. Perilaku dinamik model dianalisis dengan menentukan titik kesetimbangan dan kestabilan lokal di sekitar titik kesetimbangan. Selanjutnya, dilakukan simulasi numerik di sekitar titik kesetimbangan koeksistensi baik untuk kasus efek Allee kuat maupun efek Allee lemah. Hasil simulasi menunjukkan bahwa solusi konvergen menuju titik kesetimbangan yang artinya kedua populasi mangsa dan pemangsa dapat hidup berdampingan dan tidak akan punah sampai waktu t menuju tak terhingga. Selain itu, kondisi awal populasi mangsa dan pemangsa juga berpengaruh terhadap perilaku dinamik model.

Keywords

Collaboration network of the authors

36 authors · 71 co-authorship links

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • State University of Makassar
  • Hasanuddin University
  • 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
Hukmah HukmahAffiliation unknown2
I Nyoman WidanaAffiliation unknown1
Ita FitriaAffiliation unknown1
Agustinus RibalAffiliation unknown1
Muh HamzahAffiliation 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
Naimah ArisAffiliation unknown1
Muhammad Nur HidayatAffiliation unknown1
Nita AnggrianiAffiliation unknown1
Hendra MesraHasanuddin University1
. HendraAffiliation unknown1
Iman Al FajriAffiliation unknown1
Andi Utari SamsirAffiliation 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">Dynamics Analysis of Predator-Prey Model with Double Allee Effects and Holling Type II Functional Response</dc:title>
	<dc:title xml:lang="id">Analisis Dinamik Model Mangsa Pemangsa dengan Efek Allee Ganda dan Fungsi Respon Holling Tipe II </dc:title>
	<dc:creator xml:lang="en">Syarif, Ismi Ra'yan</dc:creator>
	<dc:creator xml:lang="en">Toaha, Syamsuddin </dc:creator>
	<dc:creator xml:lang="en">Kusuma, Jeffry </dc:creator>
	<dc:subject xml:lang="en">Predator-Prey</dc:subject>
	<dc:subject xml:lang="en">Double Allee Effect</dc:subject>
	<dc:subject xml:lang="en">Functional Response</dc:subject>
	<dc:subject xml:lang="en">Holling Type II</dc:subject>
	<dc:subject xml:lang="id">Mangsa Pemangsa</dc:subject>
	<dc:subject xml:lang="id">Efek Allee Ganda</dc:subject>
	<dc:subject xml:lang="id">Fungsi Respon</dc:subject>
	<dc:subject xml:lang="id">Holling Tipe II</dc:subject>
	<dc:description xml:lang="en">In this article, a predator prey model with double Allee effects and Holling type II functional response is discussed. Strong and weak Allee effects were analyzed separately. The dynamic behavior of the model is analyzed by determining the equilibrium point and stability around the equilibrium point. From the analysis result, it is obtained that the trivial equilibrium point is locally asymptotically stable for the case of the strong Allee effect and the saddle unstable for the case of the weak Allee effect, while the boundary and coexistence equilibrium points are locally asymptotically stable if it satisfies several parameter conditions. Numerical simulations are carried out around the coexistence equilibrium point. The simulation results show that the Allee effect threshold affects prey population growth when experiencing a strong Allee effect. The growth of the prey population also depends on the initial conditions of the prey and predator population density. Furthermore, when the prey population experiences a weak Allee effect, there is no threshold must be exceeded for the population to survive so that for each initial condition however, the population will not experience extinction.</dc:description>
	<dc:description xml:lang="id">Pada artikel ini dibahas model mangsa pemangsa dengan efek Allee ganda dan fungsi respon Holling tipe II. Efek Allee kuat dan lemah dianalisis secara terpisah. Perilaku dinamik model dianalisis dengan menentukan titik kesetimbangan dan kestabilan lokal di sekitar titik kesetimbangan. Selanjutnya, dilakukan simulasi numerik di sekitar titik kesetimbangan koeksistensi baik untuk kasus efek Allee kuat maupun efek Allee lemah. Hasil simulasi menunjukkan bahwa solusi konvergen menuju titik kesetimbangan yang artinya kedua populasi mangsa dan pemangsa dapat hidup berdampingan dan tidak akan punah sampai waktu t menuju tak terhingga. Selain itu, kondisi awal populasi mangsa dan pemangsa juga berpengaruh terhadap perilaku dinamik model.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2022-05-15</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/19237</dc:identifier>
	<dc:identifier>10.20956/j.v18i3.19237</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 18 No. 3 (2022): MAY, 2022; 434-446</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/19237/8152</dc:relation>
	<dc:relation>10.20956/j.v18i3.19237.g8152</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2022 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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