Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey
We studied the Leslie-Gower model of predator-prey with herd behavior. The square root functional response models predator and prey interactions that show herd behavior. This study aims to determine the formulation of the predator-prey model with herd behavior on prey, knowing the fixed points and i...
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| Format: | Article |
| Language: | English |
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UIN Syarif Hidayatullah
2022-04-01
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| Series: | InPrime |
| Subjects: | |
| Online Access: | https://journal.uinjkt.ac.id/index.php/inprime/article/view/24464 |
| _version_ | 1797293202370199552 |
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| author | M. Adib Jauhari Dwi Putra Ade Ima Afifa Himayati |
| author_facet | M. Adib Jauhari Dwi Putra Ade Ima Afifa Himayati |
| author_sort | M. Adib Jauhari Dwi Putra |
| collection | DOAJ |
| description | We studied the Leslie-Gower model of predator-prey with herd behavior. The square root functional response models predator and prey interactions that show herd behavior. This study aims to determine the formulation of the predator-prey model with herd behavior on prey, knowing the fixed points and its stability and simulating the model numerically. We found three fixed points that may exist: the extinction point of both species, the extinction of predator point, and the point of coexistence of the two species. The extinction of predator points is always unstable, while the point of coexistence of the two species can be stable under certain conditions. Due to the presence of square roots, the behavior of the solutions near the extinction point of the two species is not readily apparent. Numeric simulation shows that changing the initial condition and parameters can change the system's stability.
Keywords: predator-prey; functional response; herd behavior; square root functional response, Leslie-Gower model.
Abstrak
Artikel membahas model predator prey Leslie-Gower dengan perilaku bergerombol pada prey. Interaksi predator dan prey yang menunjukkan perilaku bergerombol dimodelkan dengan fungsi respon akar kuadrat. Penelitian ini bertujuan untuk mengetahui formulasi model predator-prey dengan perilaku bergerombol pada prey, mengetahui titik ekuilibrium dan kestabilannya serta menyimulasikan model tersebut secara numerik. Hasil menunjukkan terdapat tiga titik tetap yang mungkin eksis, yaitu titik kepunahan kedua spesies, titik kepunahan predator dan titik koeksistensi kedua spesies. Titik kepunahan predator selalu tidak stabil, sedangkan titik koeksistensi kedua spesies bisa stabil dengan syarat tertentu. Karena adanya akar kuadrat, perilaku solusi di dekat titik kepunahan kedua spesies tidak mudah terlihat. Simulasi numerik menunjukkan bahwa perubahan nilai awal dan parameter dapat mengubah kestabilan sistem.
Kata Kunci: predator prey; fungsi respons; perilaku bergerombol; fungsi respon akar kuadrat; model Leslie-Gower. |
| first_indexed | 2024-03-07T20:09:28Z |
| format | Article |
| id | doaj.art-fb0ab8d4b24b429291525b865d3b0870 |
| institution | Directory Open Access Journal |
| issn | 2686-5335 2716-2478 |
| language | English |
| last_indexed | 2024-03-07T20:09:28Z |
| publishDate | 2022-04-01 |
| publisher | UIN Syarif Hidayatullah |
| record_format | Article |
| series | InPrime |
| spelling | doaj.art-fb0ab8d4b24b429291525b865d3b08702024-02-28T02:16:03ZengUIN Syarif HidayatullahInPrime2686-53352716-24782022-04-0141657110.15408/inprime.v4i1.244649176Stability Analysis of Leslie-Gower Model with Herd Behavior on PreyM. Adib Jauhari Dwi Putra0Ade Ima Afifa Himayati1Department of Mathematics, Universitas Muhammadiyah KudusDepartment of Mathematics, Universitas Muhammadiyah KudusWe studied the Leslie-Gower model of predator-prey with herd behavior. The square root functional response models predator and prey interactions that show herd behavior. This study aims to determine the formulation of the predator-prey model with herd behavior on prey, knowing the fixed points and its stability and simulating the model numerically. We found three fixed points that may exist: the extinction point of both species, the extinction of predator point, and the point of coexistence of the two species. The extinction of predator points is always unstable, while the point of coexistence of the two species can be stable under certain conditions. Due to the presence of square roots, the behavior of the solutions near the extinction point of the two species is not readily apparent. Numeric simulation shows that changing the initial condition and parameters can change the system's stability. Keywords: predator-prey; functional response; herd behavior; square root functional response, Leslie-Gower model. Abstrak Artikel membahas model predator prey Leslie-Gower dengan perilaku bergerombol pada prey. Interaksi predator dan prey yang menunjukkan perilaku bergerombol dimodelkan dengan fungsi respon akar kuadrat. Penelitian ini bertujuan untuk mengetahui formulasi model predator-prey dengan perilaku bergerombol pada prey, mengetahui titik ekuilibrium dan kestabilannya serta menyimulasikan model tersebut secara numerik. Hasil menunjukkan terdapat tiga titik tetap yang mungkin eksis, yaitu titik kepunahan kedua spesies, titik kepunahan predator dan titik koeksistensi kedua spesies. Titik kepunahan predator selalu tidak stabil, sedangkan titik koeksistensi kedua spesies bisa stabil dengan syarat tertentu. Karena adanya akar kuadrat, perilaku solusi di dekat titik kepunahan kedua spesies tidak mudah terlihat. Simulasi numerik menunjukkan bahwa perubahan nilai awal dan parameter dapat mengubah kestabilan sistem. Kata Kunci: predator prey; fungsi respons; perilaku bergerombol; fungsi respon akar kuadrat; model Leslie-Gower.https://journal.uinjkt.ac.id/index.php/inprime/article/view/24464predator-preyfunctional responseherd behaviorsquare root functional response, leslie-gower model |
| spellingShingle | M. Adib Jauhari Dwi Putra Ade Ima Afifa Himayati Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey InPrime predator-prey functional response herd behavior square root functional response, leslie-gower model |
| title | Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey |
| title_full | Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey |
| title_fullStr | Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey |
| title_full_unstemmed | Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey |
| title_short | Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey |
| title_sort | stability analysis of leslie gower model with herd behavior on prey |
| topic | predator-prey functional response herd behavior square root functional response, leslie-gower model |
| url | https://journal.uinjkt.ac.id/index.php/inprime/article/view/24464 |
| work_keys_str_mv | AT madibjauharidwiputra stabilityanalysisoflesliegowermodelwithherdbehavioronprey AT adeimaafifahimayati stabilityanalysisoflesliegowermodelwithherdbehavioronprey |