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InPrime: Indonesian Journal Of Pure And Applied Mathematics
Published by Universitas Islam Negeri Syarif Hidayatullah Jakarta
ISSN : 26865335     EISSN : 27162478     DOI : 10.15408/inprime
Core Subject : Science, Education,
Computer Science & IT Mathematics
InPrime: Indonesian Journal of Pure and Applied Mathematics is a peer-reviewed journal and published on-line two times a year in the areas of mathematics, computer science/informatics, and statistics. The journal stresses mathematics articles devoted to unsolved problems and open questions arising in chemistry, physics, biology, engineering, behavioral science, and all applied sciences. All articles will be reviewed by experts before accepted for publication. Each author is solely responsible for the content of published articles. This scope of the Journal covers, but not limited to the following fields: Applied probability and statistics, Stochastic process, Actuarial, Differential equations with applications, Numerical analysis and computation, Financial mathematics, Mathematical physics, Graph theory, Coding theory, Information theory, Operation research, Machine learning and artificial intelligence.
Arjuna Subject : Matematika - Matematika Terapan
Articles 197 Documents
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Uncoupled Two Agents Modeling Via Bilinear Optimal Control Tjahjana, R. Heru
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.v4i1.24969

Abstract

In this paper, uncoupled two agents modeling is proposed using an optimal bilinear control approach. The model is proposed using assumptions: an absence of the multi agent leader, each agent cannot control the others, each agent never collides with the others, and each agent has the same properties. The special functional cost consisting of a repellent cost is considered. The Pontryagin Maximum Principle is used to determine the optimal path for each agent. After control and optimal path for each agent are obtained some of the simulation results are exposed in this paper.Keywords: uncoupled agent; modeling; bilinear system. AbstrakDalam penelitian ini, pemodelan dua agen yang tidak berpasangan disajikan dengan pendekatan kontrol optimal bilinear. Model yang diusulkan dalam paper ini ditulis dengan asumsi: tidak adanya pemimpin dalam sistem multi agen, setiap agen tidak dapat mengendalikan atau mempengaruhi agen yang lain, setiap agen tiak boleh bertabrakan satu sama lain, dan para agen mempunyai sifat-sifat yang identik. Fungsional biaya khusus yang membuat para agen tidak bertabrakan dipertimbangkan dalam penulisan paper ini. Prinsip maksimum Pontryagin digunakan dalam penentuan lintasan optimal dari para agen.  Beberapa hasil simulasi disajikan dalam paper ini.Kata Kunci: agen tak berpasangan; pemodelan; sistem bilinear.
Generalized Space Time Autoregressive (GSTAR) Model for Air Temperature Forecasting in the South Sumatera, Riau, and Jambi Provinces Aprianti, Ayu; Faulina, Naflah; Usman, Mustofa
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 6, No 1 (2024)
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.v6i1.36049

Abstract

Over the past few years, there has been a significant increase in air temperatures in regions such as South Sumatera, Riau, and Jambi, posing threats of drought, water resource crises, and erratic weather patterns. In response, developing air temperature forecasting techniques becomes imperative for effective climate change management. This study proposes implementing the Generalized Space Time Autoregressive (GSTAR) model as a practical approach for forecasting air temperatures in these regions using two weighting methods, i.e., inverse distance and normalized cross-correlation weighting. The GSTAR model, an extension of the Space Time Autoregressive (STAR) model, offers enhanced complexity by incorporating specific time and location factors, thereby increasing forecasting flexibility. The result reveals that GSTAR(1,1) with normalized cross-correlation weighting is the most optimal model, with a Root Mean Square Error (RMSE) value of 3.135, indicating high forecasting accuracy. The selection of this model is grounded in the geographical proximity and similarity of environmental characteristics of the three regions. This research contributes novel insights into the underlying mechanisms of air temperature dynamics in neighboring areas, providing a robust foundation for formulating effective policy and mitigation strategies in addressing climate change challenges.Keywords: Air temperatures, Normalized cross-correlation weighting, GSTAR(1,1), Inverse distance weighting. AbstrakDalam beberapa tahun terakhir, suhu udara mengalami peningkatan signifikan di wilayah-wilayah seperti Sumatera Selatan, Riau, dan Jambi, yang mengancam kekeringan, krisis sumber daya air, dan perubahan pola cuaca yang tidak terduga. Menghadapi situasi tersebut, pengembangan teknik peramalan suhu udara diperlukan untuk mengantisipasi dan mengelola dampak ekstrem dari perubahan iklim. Studi ini mengusulkan implementasi model Generalized Space Time Autoregressive (GSTAR) sebagai pendekatan praktis untuk meramalkan suhu udara di wilayah-wilayah tersebut menggunakan dua metode pembobotan yaitu pembobotan invers jarak dan normali korelasi silang. Model GSTAR, sebagai perluasan dari model Space Time Autoregressive (STAR), menawarkan kompleksitas yang lebih baik dengan menggabungkan faktor-faktor waktu dan lokasi tertentu, sehingga meningkatkan fleksibilitas dalam ramalan. Hasil analisis menunjukkan bahwa GSTAR(1,1) dengan pemberian bobot normalisasi korelasi silang merupakan model yang paling optimal, dengan nilai Root Mean Square Error (RMSE) sebesar 3.135, menandakan tingkat akurasi yang tinggi. Pemilihan model ini didasarkan pada kedekatan geografis dan kesamaan karakteristik lingkungan dari ketiga wilayah tersebut. Penelitian ini memberikan wawasan baru dalam mekanisme dinamika suhu udara di wilayah-wilayah yang berdekatan, serta memberikan dasar yang kuat bagi perumusan kebijakan dan strategi mitigasi yang efektif dalam menghadapi tantangan perubahan iklim.Kata Kunci: Bobot invers jarak, Bobot normalisasi korelasi silang, GSTAR(1,1), Suhu udara. 2020MSC: 62P30
Copula in Wildfire Analysis: A Systematic Literature Review Najib, Mohamad Khoirun; Nurdiati, Sri; Sopaheluwakan, Ardhasena
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 3, No 2 (2021)
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.v3i2.22131

Abstract

AbstractCopula model is a method that can be implemented in various study fields, including analyzing wildfires. The copula distribution function gives a simple way to define joint distribution between two or more random variables. This study aims to review the application of copula in the analysis of wildfires using a Systematic Literature Review (SLR) and provide insight into research opportunities related to the application in Indonesia. The results show there are very few articles using the copula model in the analysis of wildfires. However, the increasing number of article citations each year shows the importance of such article research and has contributed to wildfire analysis development. In that article, 50% of studies applied the copula model to direct wildfire analysis (using fire data) in Canada, Portugal, and the US. Meanwhile, the other 50% use the copula model for indirect wildfire analysis (not using fire data) in Canada and the European region. The outcome of the presented review will provide the latest research positions and future research opportunities on the application of copula in the analysis of wildfires in Indonesia.Keywords: copula; wildfire; systematic literature review. AbstrakModel copula merupakan metode yang dapat diimplementasikan pada berbagai bidang penelitian, salah satunya pada analisis kebakaran hutan. Fungsi sebaran copula memberikan cara yang mudah untuk mendefinisikan sebaran peluang bersama antara dua peubah acak atau lebih. Tujuan penelitian ini mengulas penerapan model copula tersebut pada analisis kebakaran hutan dalam studi literatur menggunakan Systematic Literature Review (SLR) serta memberikan peluang riset ke depan terkait implementasinya pada analisis kebakaran hutan di Indonesia. Hasil penelitian menunjukkan bahwa model copula pada analisis kebakaran hutan masih sangat sedikit. Namun, peningkatan jumlah sitasi artikel tiap tahun menunjukkan pentingnya penelitian tersebut dan memiliki kontribusi pada perkembangan analisis kebakaran hutan. Pada artikel tersebut, sebanyak 50% penelitian menerapkan model copula pada analisis kebakaran secara langsung (menggunakan data kebakaran) di Kanada, Portugal, dan Amerika. Sementara, sebanyak 50% lainnya menerapkan model copula pada analisis kebakaran secara tak langsung (tidak menggunakan data kebakaran), yaitu di Kanada dan kawasan Eropa. Hasil tinjauan memberikan posisi riset terkini serta usulan riset ke depan mengenai penerapan model copula untuk analisis kebakaran hutan dan lahan di Indonesia.Kata kunci: copula; kebakaran hutan; studi literatur sistematik. 
Analytical Study of the Existence of a Hopf Bifurcation in the Tumor Cell Growth Model with Time Delay Yusnaeni, A.; Kasbawati, Kasbawati; Syamsuddin, Toaha
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 3, No 1 (2021)
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.v3i1.19515

Abstract

AbstractIn this paper, we study a mathematical model of an immune response system consisting of a number of immune cells that work together to protect the human body from invading tumor cells. The delay differential equation is used to model the immune system caused by a natural delay in the activation process of immune cells. Analytical studies are focused on finding conditions in which the system undergoes changes in stability near a tumor-free steady-state solution. We found that the existence of a tumor-free steady-state solution was warranted when the number of activated effector cells was sufficiently high. By considering the lag of stimulation of helper cell production as the bifurcation parameter, a critical lag is obtained that determines the threshold of the stability change of the tumor-free steady state. It is also leading the system undergoes a Hopf bifurcation to periodic solutions at the tumor-free steady-state solution.Keywords: tumor–immune system; delay differential equation; transcendental function; Hopf bifurcation. AbstrakDalam makalah ini, dikaji model matematika dari sistem respon imun yang terdiri dari sejumlah sel imun yang bekerja sama untuk melindungi tubuh manusia dari invasi sel tumor. Persamaan diferensial tunda digunakan untuk memodelkan sistem kekebalan yang disebabkan oleh keterlambatan alami dalam proses aktivasi sel-sel imun. Studi analitik difokuskan untuk menemukan kondisi di mana sistem mengalami perubahan stabilitas di sekitar solusi kesetimbangan bebas tumor. Diperoleh bahwa solusi kesetimbangan bebas tumor dijamin ada ketika jumlah sel efektor yang diaktifkan cukup tinggi. Dengan mempertimbangkan tundaan stimulasi produksi sel helper sebagai parameter bifurkasi, didapatkan lag kritis yang menentukan ambang batas perubahan stabilitas dari solusi kesetimbangan bebas tumor. Parameter tersebut juga mengakibatkan sistem mengalami percabangan Hopf untuk solusi periodik pada solusi kesetimbangan bebas tumor.Kata kunci: sistem tumor–imun; persamaan differensial tundaan; fungsi transedental; bifurkasi Hopf.
Statistical Modeling using A New Hybrid Form of The Inverted Exponential Distribution with Different Estimation Methods Adubisi, O. D.; Adubisi, C. E.
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 4, No 2 (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.v4i2.26830

Abstract

This paper introduces a new four-parameter distribution called the exponentiated Gompertz generated inverted exponential (EGGIE) distribution. Explicit expressions of the structural properties such as the ordinary and incomplete moments, probability weighted moments, quantile function, Lorenz and Bonferroni curves, entropies, and order statistics are derived. The empirical findings indicate that the maximum likelihood procedure dominates the other estimators in the simulation study while the Cramer-Von Mises procedure dominates in the two real datasets applications. We demonstrate the superiority of the EGGIE distribution over the Gompertz Lomax, odd Fréchet Inverse exponential, generalized inverse exponential, generalized inverse exponential, exponential inverse exponential, and Gompertz Weibull distribution using the maximum likelihood procedure utilizing two real datasets applications. The findings show that the EGGIE distribution yields the best goodness of fit to the two datasets.Keywords: exponentiated Gompertz generated family; inverse exponential distribution; Kolmogorov-Smirnov statistic; Anderson-Darling; maximum product spacing. AbstrakPaper ini memperkenalkan distribusi 4-parameter baru yang disebut dengan distribusi exponentiated Gompertz generated inverted exponential (EGGIE). Ekspresi eksplisit sifat struktural dari distribusi ini diturunkan, seperti momen biasa dan momen tak lengkap, momen probabilitas terboboti, fungsi kuartil, kurva Lorenz dan Bonferroni, entropi, dan statistik urutan. Temuan empiris menunjukan bahwa prosedur maksimum likelihood mendominasi estimator lainnya pada studi simulasi, sementara prosedur Cramer-Von Mises mendominasi pada aplikasi dua dataset nyata. Peneliti menunjukkan keunggulan dari distribusi EGGIE dibandingkan distribusi Gompertz Lomax, odd Frechet Inverse exponential, generalized inverse exponential, exponential inverse exponential, dan Gompertz Weibull menggunakan metode maksimum likelihood yang diaplikasikan pada dua dataset nyata. Hasil menunjukan bahwa distribusi EGGIE menghasilkan kecocokan model yang baik pada kedua dataset.Kata Kunci: keluarga bangkitan exponentiated Gompertz; distribusi inverse exponential; Kolmogorov-Smirnov statistic; Anderson-Darling; maximum product spacing. 2020MSC: 62E10
N-Level Structural Equation Models (nSEM): The Effect of Sample Size on the Parameter Estimation in Latent Random-Intercept Model Eminita, Viarti; Saefuddin, Asep; Sadik, Kusman; Syafitri, Utami Dyah
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 6, No 1 (2024)
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.v6i1.38914

Abstract

Multilevel Structural Equation Modeling (MSEM) is claimed to address hierarchical data structures and latent response variables, but it becomes unstable with an increasing number of levels. N-Level SEM (nSEM) is an SEM framework designed to handle a growing number of levels in the model. The nSEM framework uses the Maximum Likelihood Estimation (MLE) method for parameter estimation, which requires a large sample size and correct model specification. Therefore, it is essential to consider the necessary minimal sample size to ensure accurate and efficient parameter estimation in the nSEM model. This study examined how sample size affects the performance of parameter estimators in nSEM models. We propose a method to evaluate the effect of many environments to estimate the results of factor loadings and environmental variance produced by the model. In addition, we also assess the impact of environment size on the estimation results of factor loadings and individual variance. The results were then applied to actual data on student mathematics learning motivation in Depok. The findings show that neither the number of environments nor the size of the environment affects the performance of fixed parameter estimation in the nSEM model. nSEM indicates excellent performance in estimating environmental variance at level 2 when the number of environments increases. Conversely, increasing the size of the environment worsens the performance of estimating individual variance parameters. Overall, the nSEM framework for the latent random-intercept (LatenRI) model performs well with increasing sample sizes. The application data on LatenRI models show almost similar estimation results.Keywords: Hierarchical data; Latent random intercept model; Multilevel structural equation modeling; n-Level structural equation modeling.AbstrakMultilevel Structural Equation Modeling (MSEM) diklaim dapat mengatasi struktur data hierarki dan variabel respons laten, namun menjadi tidak stabil dengan bertambahnya jumlah level. N-Level SEM (nSEM) adalah kerangka kerja SEM yang dirancang untuk menangani semakin banyak level dalam model. Kerangka kerja nSEM menggunakan metode Maximum Likelihood Estimation (MLE) untuk estimasi parameter, yang memerlukan ukuran sampel yang besar dan spesifikasi model yang benar. Oleh karena itu, penting untuk mempertimbangkan ukuran sampel minimal yang diperlukan untuk memastikan estimasi parameter yang akurat dan efisien dalam model nSEM. Studi ini menguji bagaimana ukuran sampel mempengaruhi kinerja penduga parameter dalam model nSEM. Kami mengusulkan metode untuk mengevaluasi pengaruh banyak lingkungan dalam memperkirakan hasil factor loadings  dan varians lingkungan yang dihasilkan oleh model. Selain itu, kami juga menilai dampak ukuran lingkungan terhadap hasil estimasi factor loadings dan varians individu. Hasilnya kemudian diterapkan pada data aktual motivasi belajar matematika siswa di Depok. Hasil menunjukkan bahwa baik jumlah lingkungan maupun ukuran lingkungan tidak mempengaruhi kinerja estimasi parameter tetap pada model nSEM. nSEM menunjukkan kinerja yang sangat baik dalam memperkirakan varians lingkungan pada level 2 ketika jumlah lingkungan meningkat. Sebaliknya, peningkatan ukuran lingkungan akan memperburuk kinerja pendugaan parameter varians individu. Secara keseluruhan, kerangka nSEM untuk model intersepsi acak laten (LatenRI) bekerja dengan baik dengan meningkatnya ukuran sampel. Data penerapan model LatenRI menunjukkan hasil estimasi yang hampir serupa.Kata Kunci: Data hirarki; Model intersep acak laten; Model persamaan structural multilevel; Model persamaan structural n-level. 2020MSC: 62D99
E-Cordial Labeling for Cupola Graph Cu(3, b, n) Yulianti, Kartika; Rokhmatillah, Fitri; Sispiyati, Ririn
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.v4i1.24210

Abstract

Graph labeling is a map that maps graph elements such as vertices, edges, vertices, and edges to a set of numbers. A graph labeling is named e-cordial if there is a binary mapping f:E(G)→{0,1} which induces the vertex labeling defined by g(v)=Ʃ_{uvϵE(G)}f(uv)(mod 2), so that it satisfies the absolute value of the difference between the number of vertices labeled 1 and the number of vertices labeled 0 is less than equal to 1, and also for the number of edges labeled 0 and labeled 1. A graph that admits the e-cordial labeling is called an e-cordial graph. In this paper, we proved that some of the cupola graph Cu(3,b,n) is e-cordial.Keywords: E-Cordial Labeling; E-Cordial Graph; Cupola Graph Cu(a, b, n). AbstrakPelabelan graf merupakan pemetaan yang memetakan unsur-unsur graf seperti simpul, sisi, simpul dan sisi ke himpunan bilangan. Sebuah pelabelan dinamakan pelabelan e-cordial jika terdapat pemetaan biner f:E(G)→{0,1} yang menginduksi pelabelan simpul yang didefinisikan g(v)=Ʃ_{uvϵE(G)}f(uv)(mod 2) sehingga nilai mutlak dari selisih banyaknya simpul yang dilabeli 1 dan banyaknya simpul yang dilabeli 0 kurang dari sama dengan 1, dan nilai mutlak dari selisih banyaknya sisi yang dilabeli 1 dan banyaknya sisi yang dilabeli 0 kurang dari sama dengan 1. Sebuah graf yang dapat dilabeli secara e-cordial dinamakan graf e-cordial. Pada makalah ini dibuktikan bahwa beberapa graf kubah Cu(3,b,n) adalah e-cordial.Kata Kunci : Pelabelan E-Cordial; Graf E-Cordial; Graf Kubah Cu(a, b, n).
An Optimal Control Analysis of Dengue Fever Ilmayasinta, Nur; Febriyanti, Rahma; Prafianti, Rayinda Aseti; Zakiyah, Nabila Syarifah
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 5, No 2 (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.v5i2.30392

Abstract

AbstractDengue fever is one of the most infectious diseases in the world, according to data issued by the World Health Organization in 2014. It is responsible for a huge number of deaths each year around the world, particularly in tropical nations. The dengue virus (DENV) causes dengue fever, which is spread by the female Aedes aegypti mosquito. We provide a mathematical model of dengue fever transmission through hospitalization with optimal management in this paper. Before being simulated in MATLAB, this optimum control problem is numerically resolved. Vaccination, pesticide use, and prevention are all examples of optimal control in this study. The simulation results demonstrate that dengue infection can be considerably reduced by vaccination, pesticide use, and prevention.Keywords: Dengue fever; Mathematical modelling; Optimal control. AbstrakDemam berdarah adalah salah satu penyakit paling menular di dunia, menurut data yang dikeluarkan oleh Organisasi Kesehatan Dunia pada tahun 2014. Penyakit ini menyebabkan banyak kematian setiap tahun di seluruh dunia, terutama di negara-negara tropis. Virus dengue (DENV) menyebabkan demam berdarah, yang disebarkan oleh nyamuk Aedes aegypti betina. Kami menyediakan model matematis penularan demam berdarah melalui rawat inap dengan penatalaksanaan optimal dalam makalah ini. Masalah kontrol optimal ini diselesaikan secara numerik sebelum disimulasikan di MATLAB. Vaksinasi, penggunaan pestisida, dan pencegahan merupakan contoh pengendalian yang optimal dalam penelitian ini. Hasil simulasi menunjukkan bahwa infeksi dengue dapat dikurangi dengan vaksinasi, penggunaan pestisida, dan pencegahan.Kata Kunci: Demam berdarah; Pemodelan matematika; Kontrol optimal. 2020MSC: 00A71, 92B05.
Another Antimagic Decomposition of Generalized Peterzen Graph Inayah, Nur; Musti, M. Irvan Septiar; Masyithoh, Soffi Nur
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 3, No 2 (2021)
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.v3i2.19954

Abstract

AbstractA decomposition of a graph P into a family Q consisting of isomorphic copies of a graph Q is (a,b)-Q-antimagic if there is a bijection φ:V(P)∪E(P)→{1,2,3,4…,v_P+e_P} such that for all subgraphs Q’ isomorphic to Q,   the Q-weightsφ(Q’ )=∑_(v∈V(Q^' ))▒φ(v) + ∑_(e∈E(Q^'))▒〖φ(e)〗constitute an arithmetic progression a,a + b,a + 2b,…,a + (r - 1)b where a and b are positive integers and r is the number of subgraphs of P isomorphic to Q. In this article, we prove the existence of a (a,b)-P_4-antimagic  decomposition of a generalized Peterzen graph GPz(n,3) for several values of b.Keywords: covering; decomposition; antimagic; generalized Peterzen. AbstrakSuatu dekomposisi dari suatu graf P ke dalam suatu famili Q yang terdiri dari salinan isomorfik dari graf Q dikatakan (a,b)-Q-antiajaib jika terdapat pemetaaan bijektif φ:V(P)∪E(P)→{1,2,3,4…,v_P+e_P} sedemikian sehingga semua subgraf Q’ yang isomorfik ke Q, dengan bobot-Q sebagai berikutφ(Q’ )=∑_(v∈V(Q^' ))▒φ(v) + ∑_(e∈E(Q^'))▒〖φ(e)〗yang membentuk suatu barisan aritmatika yaitu a,a + b,a + 2b,…,a + (r - 1)b dengan a dan b adalah bilangan bulat positif dan r adalah banyaknya subgraf dari P yang isomorfik ke Q. Pada artikel ini, kami membuktikan eksistensi (a,b)-P_4-antiajaib dekomposisi dari graf generalized Peterzen GPz(n,3) untuk beberapa nilai b.Kata kunci: selimut; dekomposisi; antiajaib; generalized Peterzen.
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

Abstract

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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