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Jurnal Ilmu Dasar
Published by Universitas Jember
ISSN : 24425613     EISSN : -     DOI : https://doi.org/10.19184/jid.v24i2.36657
Core Subject : Education, Engineering,
Control & Systems Engineering Mathematics
Jurnal ILMU DASAR (JID) is a national peer-reviewed and open access journal that publishes research papers encompasses all aspects of natural sciences including Mathematics, Physics, Chemistry and Biology. JID publishes 2 issues in 1 volume per year. First published, volume 1 issue 1, in January 2000 and avalaible in electronically since 2012 with ISSN 1411-5735 (Print) and avalaible in electronically since 2012 with ISSN 2442-5613 (online). Jurnal ILMU DASAR is accredited SINTA 3 by the Ministry of Education, Culture, Research, and Technology of the Republic of Indonesia (Kemendibukristek) No. 152/E/KPT/2023 (September 25, 2023), Ministry of Research, Technology and Higher Education of the Republic of Indonesia (RISTEKDIKTI), No. 200/M/KPT/2020 (December. 23, 2020). All accepted manuscripts will be published worldwide JID has been indexed in DOAJ, Dimension, OCLC WorldCat, PKP Index, Crossref, Google Scholar, Base, Garuda, and OneSearch. JID have been collaborated in KOBI-ID (Konsorsium Biologi Indonesia) and HKI (Himpunan Kimia Indonesia) since 2017.
Arjuna Subject : Matematika - Kontrol dan Optimasi
Articles 11 Documents
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Search results for , issue "Vol 22 No 2 (2021)" : 11 Documents clear
Local Stability Dynamics of Equilibrium Points in Predator-Prey Models with Anti-Predator Behavior Harianto, Joko; Suparwati, Titik; Dewi, Alfonsina Lisda Puspa
Jurnal ILMU DASAR Vol 22 No 2 (2021)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/jid.v22i2.23991

Abstract

This article describes the dynamics of local stability equilibrium point models of interaction between prey populations and their predators. The model involves response functions in the form of Holling type III and anti-predator behavior. The existence and stability of the equilibrium point of the model can be obtained by reviewing several cases. One of the factors that affect the existence and local stability of the model equilibrium point is the carrying capacity (k) parameter. If x3∗, y3∗ > 0 is a constant solution of the model and ∈ (0,x3∗), then there is a unique boundary equilibrium point Ek (k , 0). Whereas, if k ∈ (x4∗, y4∗], then Ek (k, 0) is unstable and E3 (x3∗, y3∗) is stable. Furthermore, if k ∈ ( x4∗, ∞), then Ek ( k, 0) remains stable and E4 (x4∗, y4∗) is unstable, but the stability of the equilibrium point E3 (x3∗, y3∗) is branching. The equilibrium point E3 (x3∗, y3∗) can be stable or unstable depending on all parameters involved in the model. Variations of k parameter values are given in numerical simulation to verify the results of the analysis. Numerical simulation indicates that if k = 0,92 then nontrivial equilibrium point Ek (0,92 ; 0) stable. If k = 0,93 then Ek (0,93 ; 0) unstable and E3∗(0,929; 0,00003) stable. If k = 23,94, then Ek (23,94 ; 0) and E3∗(0,929; 0,143) stable, but E4∗(23,93 ; 0,0005) unstable. If k = 38 then Ek(38,0) stable, but E3∗(0,929; 0,145) and E4∗(23,93 ; 0,739) unstable.Keywords: anti-predator behavior, carrying capacity, and holling type III.

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