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All Journal Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Bulletin of Applied Mathematics and Mathematics Education
Trimanto, Rido
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Mathematics

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MODEL FRAKSIONAL PREDATOR-PREY PADA KAWASAN KONSERVASI PERAIRAN Trimanto, Rido; Adi, Yudi Ari
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 15 No 2 (2023): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2023.15.2.7853

Abstract

ABSTRACT. This paper discusses predator-prey models in water conservation areas in fractional order using Caputo Fabrizio derivatives. The purpose of this research is to study population dynamics in conservation areas. Based on the model, we obtain three equilibrium points. From the analysis of the model, it is found that the extinction equilibrium point of all subpopulations is unstable. Meanwhile, the equilibrium point for the extinction of predator populations is local asymptotic stability under certain conditions. Furthermore, in a certain condition, the coexistence of predator and prey equilibrium points is globally asymptotically stable. Numerical simulations were performed using the Adams Bashfort three-step method with the Caputo Fabrizio derivative to support the theoretical results. Simulations show that the smaller the order, the faster the population converges to the equilibrium pointKeywords: Predator-prey model, conservation area, fractional order, equilibrium, stability. ABSTRAK. Makalah ini membahas model pemangsa-mangsa di kawasan konservasi perairan dalam orde fraksional menggunakan turunan Caputo Fabrizio. Tujuan dari penelitian ini adalah untuk mempelajari dinamika populasi di kawasan konservasi. Berdasarkan model, kami memperoleh tiga titik kesetimbangan. Dari model tersebut diperoleh bahwa titik kesetimbangan kepunahan semua subpopulasi tidak stabil. Sementara iti, titik keseimbangan kepunahan populasi predator adalah stabil asimtotik lokal dengan kondisi tertentu. Selanjutnya untuk titik kesetimbangan dengan semua populasi ada stabil secara global asimtotik jika memenuhi kondisi tertentu. Simulasi numerik dilakukan dengan menggunakan metode Adams Bashfort tiga langkah dengan turunan Caputo Fabrizio untuk mendukung hasil teoritis. Simulasi menunjukkan bahwa semakin kecil order semakin mempercepat populasi konvergen ke titik kesetimbangan.Kata Kunci: Model pemangsa-mangsa, kawasan konservasi, orde fractional, kesetimbangan, kestabilan
Indonesian provincial clustering using Elbow method for the national food security during pandemic Trimanto, Rido; Yustari, Eryka; Nafisah, Zulfatin; Carolina, Nona; Irsalinda, Nursyiva; Setyorini, Arifah Indah
Bulletin of Applied Mathematics and Mathematics Education Vol. 2 No. 2 (2022)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/bamme.v2i2.6166

Abstract

The Covid-19 pandemic had an impact on the joints of socio-economic life, especially in fulfilling the basic needs. It also caused the declining of global food security, especially in Indonesia. This study aims to develop regional mapping to determine food security priorities and to achieve equal distribution of food security throughout Indonesia. The research method used in this research is quantitative research with the Elbow method. The Elbow method is used to find the optimal cluster size. The data used are from the Food Security Agency of the Indonesian Ministry of Agriculture and Central Statistics Agency in a range of 2020 to 2021. In the process to identify priority areas in Indonesia, it is necessary to have provincial clustering. It is also necessary to minimize food budget allocations that are not well-targeted, causing losses, and not achieving an equal distribution of food security programs. Looking from a more visionary perspective, the success of clustering provides an opportunity for the government to focus more on allocating budget, resources, and time according to the results of the clustering. Based on the results of the provincial clustering, two clusters were obtained, namely provinces with high food security (Cluster 1) and low food security (Cluster 2). Cluster 1 has lower constituent components than Cluster 2.
Co-Authors Carolina, Nona Irsalinda, Nursyiva NAFISAH, ZULFATIN Setyorini, Arifah Indah Yudi Ari Adi, Yudi Ari Yustari, Eryka