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Himayati, Ade Ima Afifa

Universitas Muhammadiyah Kudus

Author-ID : 1751069

Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Industrial & Manufacturing Engineering Languange, Linguistic, Communication & Media Library & Information Science Mathematics Physics Public Health Social Sciences Other

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Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey M. Adib Jauhari Dwi Putra; Ade Ima Afifa Himayati
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 4, No 1 (2022)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v4i1.24464

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. AbstrakArtikel 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.

Research Trends in Mathematical Modeling Applied to Pandemic Cases: A Bibliometric Analysis Rosyida, Azma; Utami, Risqi; Arlinwibowo, Janu; Fatima, Gupita Nadindra; Himayati, Ade Ima Afifa
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 5, No 1 (2023)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v5i1.28873

AbstractThe disease caused by the virus has caused a continuous pandemic worldwide since 2012. In order to slow down the rapid spread of the virus, many countries have taken recovery measures. This paper aims to analyze the trends of modeling pandemic cases in Scopus-indexed journals. The research method is a literature review using a bibliometric analysis approach starting from defining the keywords modeling' and ‘pandemic' in the Publish or Perish application with Google Scholar as the database. After narrowing the results by selecting the topic of modeling the pandemic problem it consisted of 200 articles in total. After that, the metadata was compiled using the Mendeley application, the VosViewer application was used to create a research trend visualization. The results obtained by bibliometric analysis show that the number of publications continues to increase. Which journals are published, which organizations and countries publish the most, how the evolution of perspective has changed since 2012, and which articles are most cited. We conclude that since the pandemic, there is a possibility of an evolution in the quality of publications.Keywords: bibliometric analysis; pandemic; mathematical model; Mendeley; Publish or Perish; Vosviewer. AbstrakPenyakit yang diakibatkan dari virus telah menyebabkan pandemi berkelanjutan di seluruh dunia sejak 2012. Untuk memperlambat penyebaran virus yang cepat, banyak negara telah mengambil langkah pemulihan. Tulisan ini bertujuan untuk menganalisis tren pemodelan kasus pandemi di jurnal terindeks Scopus. Metode penelitian adalah kajian pustaka dengan pendekatan analisis bibliometrik dimulai dari pendefinisian kata kunci ‘pemodelan’ dan 'pandemi' pada aplikasi Publish or Perish dengan database Google Scholar. Setelah dilakukan penyempitan hasil dengan pemilihan topik pemodelan masalah pandemi maka total artikel menjadi 200 artikel. Setelah itu dilakukan kompilasi metadata menggunakan aplikasi Mendeley, aplikasi VosViewer digunakan untuk membuat visualisasi trend penelitian. Hasil yang diperoleh dengan analisis bibliometrik menunjukkan bahwa jumlah publikasi terus meningkat. Jurnal mana yang diterbitkan, organisasi dan negara mana yang paling banyak menerbitkan, bagaimana evolusi perspektif telah berubah sejak 2012, dan artikel mana yang paling banyak dikutip. Kami menyimpulkan bahwa sejak pandemi, ada kemungkinan terjadi evolusi kualitas publikasi.Kata Kunci: analisis bibliometrik; pandemi; model matematika; Mendeley; Publish or Perish; Vosviewer. 2020MSC: 00A71, 92B05.

Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey Dwi Putra, M. Adib Jauhari; Himayati, Ade Ima Afifa
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 4, No 1 (2022)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v4i1.24464

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. AbstrakArtikel 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.

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