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A Stage-Structure Rosenzweig-MacArthur Model with Effect of Prey Refuge

Jambura Journal of Biomathematics (JJBM) · Vol. ume (2020) · hlm. 1–7

DOI
10.34312/jjbm.v1i1.6891
ISSN
2723-0317
Terbit
2020-06-15
Penerbit
Department of Mathematics, Universitas Negeri Gorontalo
Bahasa
eng
Lisensi
creativecommons.org/licenses/by-nc/4.0

Abstrak

We proposed and analyzed a stage-structure Rosenzweig-MacArthur model incorporating a prey refuge. It is assumed that the prey is a stage-structure population consisting of two compartments known as immature prey and mature prey. The model incorporates the functional response Holling type-II. In this work, we investigate all the biologically feasible equilibrium points, and it is shown that the system has three equilibrium points. Sufficient conditions for the local stability of the non-negative equilibrium point of the model are also derived. All points are conditionally locally asymptotically stable. By constructing Jacobian matrix and determined eigenvalues, we analyzed the local stability of the trivial equilibrium and non-predator equilibrium points. Specifically for coexistence equilibrium point, Routh-Hurwitz criterion used to analyze local stability. In addtion, we investigated the effect of immature prey refuge. Our mathematical analysis exhibits that immature prey refuge have played a crucial role in the behavioral system. When the effect of immature prey refuge (constant m) increases, it is can stabilize non-predator equilibrium point, where all the species can not exists together. And conversely, if contant m decreases, it is can stabilize coexistence equilibrium point then all the species can exists together. The work is completed with a numerical simulation to confirmed analitical results

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  • Universitas Pattimura
  • State University of Malang
  • State University of Gorontalo
  • Sekolah Tinggi Ilmu Kesehatan Pasapua Ambon
  • University of South Africa
  • Universitas Pembangunan Nasional Veteran Yogyakarta
  • University of Medical Sciences, Ondo
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Rekan penulisOrganisasiArtikel bersama
Venn Yan Ishak IlwaruUniversitas Pattimura3
Yopi Andry LesnussaUniversitas Pattimura2
Muhammad Fandi AnsoriDiponegoro University2
Lusye BakarbessyUniversitas Pattimura2
Monce DahokloryUniversitas Pattimura2
Sri Lestari RahayuState University of Malang1
Fauziatul FajarohState University of Malang1
Sumari SumariState University of Malang1
Vynska Amalia PermadiUniversitas Pembangunan Nasional Veteran Yogyakarta1
Olumuyiwa James PeterUniversity of Medical Sciences, Ondo1
Maria Engeline SahusilawaneUniversitas Pattimura1
Mayowa M. OjoUniversity of South Africa1
Emli RahmiState University of Gorontalo1
Hasan S. PanigoroState University of Gorontalo1
Dian SavitriUniversitas Negeri Surabaya1
Dorteus L. RahakbauwUniversitas Pattimura1
Monalisa E. RijolyUniversitas Pattimura1
Abraham Z. WattimenaUniversitas Pattimura1
Zeth Arthur LeleuryUniversitas Pattimura1

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Sumber metadata: OAI-PMH (metadata jurnal) http://ejurnal.ung.ac.id/index.php/JJBM/oai, pertama di-harvest 9 Nov 2026, terakhir terlihat 9 Nov 2026.
Metadata asli (oai_dc) 
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	<dc:title xml:lang="en-US">A Stage-Structure Rosenzweig-MacArthur Model with Effect of Prey Refuge</dc:title>
	<dc:creator>Beay, Lazarus Kalvein</dc:creator>
	<dc:creator>Saija, Maryone</dc:creator>
	<dc:subject xml:lang="en-US">Rosenzweig-MacArthur Model; Stage-Structure; Refuge; Routh-Hurwitz Criterion</dc:subject>
	<dc:description xml:lang="en-US">We proposed and analyzed a stage-structure Rosenzweig-MacArthur model incorporating a prey refuge.  It is assumed that the prey is a stage-structure population consisting of two compartments known as immature prey and mature prey. The model incorporates the functional response Holling type-II. In this work, we investigate all the biologically feasible equilibrium points, and it is shown that the system has three equilibrium points. Sufficient conditions for the local stability of the non-negative equilibrium point of the model are also derived. All points are conditionally locally asymptotically stable. By constructing Jacobian matrix and determined eigenvalues, we analyzed the local stability of the trivial equilibrium and non-predator equilibrium points. Specifically for coexistence equilibrium point, Routh-Hurwitz criterion used to analyze local stability. In addtion, we investigated the effect of immature prey refuge. Our mathematical analysis exhibits that immature prey refuge have played a crucial role in the behavioral system. When the effect of immature prey refuge (constant m) increases, it is can stabilize non-predator equilibrium point, where all the species can not exists together. And conversely, if contant m decreases, it is can stabilize coexistence equilibrium point then all the species can exists together. The work is completed with a numerical simulation to confirmed analitical results</dc:description>
	<dc:publisher xml:lang="en-US">Department of Mathematics, Universitas Negeri Gorontalo</dc:publisher>
	<dc:contributor xml:lang="en-US"></dc:contributor>
	<dc:date>2020-06-15</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:type xml:lang="en-US">Peer-reviewed Article</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://ejurnal.ung.ac.id/index.php/JJBM/article/view/6891</dc:identifier>
	<dc:identifier>10.34312/jjbm.v1i1.6891</dc:identifier>
	<dc:source xml:lang="en-US">Jambura Journal of Biomathematics (JJBM); Volume 1, Issue 1: June 2020; 1-7</dc:source>
	<dc:source>2723-0317</dc:source>
	<dc:source>10.34312/jjbm.v1i1</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ejurnal.ung.ac.id/index.php/JJBM/article/view/6891/2112</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2020 Lazarus Kalvein Beay; Maryone Saija</dc:rights>
	<dc:rights xml:lang="en-US">https://creativecommons.org/licenses/by-nc/4.0</dc:rights>
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