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DYNAMICAL BEHAVIOR IN THE COMPETITIVE MODEL INCORPORATING THE FEAR EFFECT OF PREY DUE TO ALLELOPATHY WITH SHARED BIOTIC RESOURCES

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 18 No. 4 (2024) · hlm. 2663–2674

DOI
10.30598/barekengvol18iss4pp2663-2674
ISSN
2615-3017, 1978-7227
Terbit
2024-10-14
Penerbit
PATTIMURA UNIVERSITY
Bahasa
eng
Lisensi
creativecommons.org/licenses/by-sa/4.0

Abstrak

This research develops a mathematical model of a natural phenomenon, namely sea snails that can release toxins (allelopathy) so that non-toxic sea snails become afraid. In addition, toxic and non-toxic sea snails share biotic resources. Based on the existing phenomenon, the model of fear effect caused by allelopathy in the competitive interaction model with shared biotic resources will be studied. In this system, three equilibrium points are obtained: extinction point of prey, extinction point of predator, and coexisting point under certain conditions. Analysis of local stability at equilibrium points by linearization shows that all equilibrium points are asymptotically stable with certain conditions. Numerical simulations at the equilibrium point show the same results as the analysis results. Then, numerical continuity was carried out by selecting variation of the fear effect parameter for Numerical continuity results show that changes in these parameters affect the population of toxic and non-toxic species, marked by the emergence of Transcritical bifurcations, Bifurcation occurs at the first Saddle-Node bifurcation at and the second Saddle-Node bifurcation at

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  • Universitas Negeri Surabaya
  • Diponegoro University
  • Atma Jaya Catholic University of Indonesia
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Rekan penulisOrganisasiArtikel bersama
Siti SaadahAtma Jaya Catholic University of Indonesia2
Siti Maghfirotun AminUniversitas Negeri Surabaya1
Abd Kadir JaelaniAfiliasi tidak diketahui1
Rudianto ArtionoAfiliasi tidak diketahui1
Budi Priyo PrawotoAfiliasi tidak diketahui1
Phobe AndreaniAfiliasi tidak diketahui1
Sri Harini EkowatiAfiliasi tidak diketahui1
Ninuk LustyantieAfiliasi tidak diketahui1
Sri MulyaniDiponegoro University1
Vernanda ApriliaAfiliasi tidak diketahui1
Retno Ekawati NingrumAfiliasi tidak diketahui1
Yuliani Puji AstutiAfiliasi tidak diketahui1

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Sumber metadata: OAI-PMH (metadata jurnal) https://ojs3.unpatti.ac.id/index.php/barekeng/oai, pertama di-harvest 5 Nov 2026, terakhir terlihat 5 Nov 2026.
Metadata asli (oai_dc) 
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	<dc:title xml:lang="en-US">DYNAMICAL BEHAVIOR IN THE COMPETITIVE MODEL INCORPORATING THE FEAR EFFECT OF PREY DUE TO ALLELOPATHY WITH SHARED BIOTIC RESOURCES</dc:title>
	<dc:creator>Dewi, Mifta Kharisma</dc:creator>
	<dc:creator>Savitri, Dian</dc:creator>
	<dc:creator>Abadi, Abadi</dc:creator>
	<dc:description xml:lang="en-US">This research develops a mathematical model of a natural phenomenon, namely sea snails that can release toxins (allelopathy) so that non-toxic sea snails become afraid. In addition, toxic and non-toxic sea snails share biotic resources. Based on the existing phenomenon, the model of fear effect caused by allelopathy in the competitive interaction model with shared biotic resources will be studied. In this system, three equilibrium points are obtained: extinction point of prey, extinction point of predator, and coexisting point under certain conditions. Analysis of local stability at equilibrium points by linearization shows that all equilibrium points are asymptotically stable with certain conditions. Numerical simulations at the equilibrium point show the same results as the analysis results. Then, numerical continuity was carried out by selecting variation of the fear effect parameter for  &amp;nbsp;Numerical continuity results show that changes in these parameters affect the population of toxic and non-toxic species, marked by the emergence of Transcritical bifurcations, Bifurcation occurs at &amp;nbsp;the first Saddle-Node bifurcation at  &amp;nbsp;and the second Saddle-Node bifurcation at </dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2024-10-14</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://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13442</dc:identifier>
	<dc:identifier>10.30598/barekengvol18iss4pp2663-2674</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application; 2663-2674</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol18iss4year2024</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13442/8884</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2024 Mifta Kharisma Dewi, Dian Savitri, Abadi Abadi</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
</oai_dc:dc>