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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Musamus Journal of Mathematics Education
Ruslau, Maria F. V.
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Mathematics

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Meningkatkan Kemampuan Pemecahan Masalah Matematika Siswa pada Materi SPLDV (Pakaian Tradisional Suku Mee) Doo, Katarina Clara; Ruslau, Maria F. V.; Untayana, Juliana R.
Musamus Journal of Mathematics Education Vol 6 No 2 (2024): Musamus Journal of Mathematics Education
Publisher : Musamus University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35724/musamus journal of mathematics education.v6i2.6120

Abstract

Dalam pembelajaran matematika pada materi SPLDV sering ditemukan siswa yang masih mengalami kesulitan dalam pemecahan masalah matematika. Kesulitan tersebut terjadi karena kurangnya siswa dalam memecahkan masalah dengan tepat pada materi SPLDV. Masalah ini diperlukan adanya tindakan untuk meningkatkan kemampuan pemecahan masalah matematika. Atas dasar permasalahan, penelitian ini bertujuan meningkatkan kemampuan dalam pemecahan masalah matematika siswa pada materi SPLDV. Penelitian ini menggunakan masalah pakaian adat, yang disesuaikan dengan karakteristik atau kompetensi jususan tata busana, dengan harapan siswa lebih mudah menerjemahkan masalah dalam konteks matematika. Jenis penelitian ini merupakan Penitilian Tindakan Kelas yang dilaksanakan dalam dua siklus. Indikator pemecahan masalah dalam penelitian ini meliputi memahami masalah, menentukan gambaran penyelesaian masalah, menyelesaikan masalah, dan pengecekan kembali. Penelitian akan dipastikan berhasil apabila memenuhi syarat adalah: (1) kemampuan pemecahan masalah matematika siswa pada siklus pertama meningkat dari pra siklus dan juga siklus satu ke siklus dua, (2) persentase kemampuan penyelesaian pemecahan masalah matematika siswa tuntas minimal 75%. Pencapaian penelitian memperoleh rata-rata kemampuan pra siklus siswa adalah 62. Siklus I mengalami peningkatan menjadi 70,75 dan pada siklus II mengalami peningkatan menjadi 86,5. Berdasarkan hasil penelitian disimpulkan bahwa dapat meningkatkan kemampuan pemecahan masalah matematika siswa pada materi SPLDV kelas X Tata Busana SMK Negeri 2 Pariwisata Merauke.
Analysis Dynamics Model Predator-Prey with Holling Type III Response Function and Anti-Predator Behavior Pratama, Rian Ade; Suryani, Dessy Rizki; Ruslau, Maria F. V.; Meirista, Etriana; Nurhayati, Nurhayati
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 3 (2025): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i3.31533

Abstract

Understanding predator-prey dynamics is essential for maintaining ecological balance and biodiversity. Classical models often fail to capture complex biological behaviors such as prey defense mechanisms and nonlinear predation effects, which are vital for accurately describing real ecosystems. In light of this, there is a growing need to incorporate behavioral and functional complexity into mathematical models to better understand species interactions and their long-term ecological outcomes. This study aims to develop and analyze a predator-prey model that integrates two key ecological features: a Holling type III functional response and the anti-predator behavior exhibited by prey. The model assumes a habitat with limited carrying capacity to reflect environmental constraints. We formulate a nonlinear system of differential equations representing the interaction between prey and predator populations. The model is examined analytically by identifying equilibrium points and analyzing their local stability using the Routh-Hurwitz criteria. A literature-based theoretical analysis is supplemented with numerical simulations to validate and illustrate population dynamics. The model exhibits three equilibrium points: a trivial solution (extinction), a predator-free equilibrium, and a non-trivial saddle point representing coexistence. The non-trivial equilibrium best reflects ecological reality, indicating stable coexistence where prey consumption is balanced by reproduction, and predator mortality aligns with energy intake. Numerical simulations show that prey populations initially grow rapidly, then decline as they reach carrying capacity, while predator populations grow after a time lag and eventually stabilize. The results are further supported by the eigenvalue analysis, confirming local asymptotic stability. The proposed model realistically captures predator-prey dynamics, demonstrating that the inclusion of anti-predator behavior and a Holling type III response significantly affects population trajectories and system stability. This framework provides a more ecologically valid approach for studying long-term species coexistence and highlights the importance of incorporating behavioral responses in ecological modeling.
Trajectories of Cannibalism Interaction with Holling Type II and Monod–Haldane Functional Responses Pratama, Rian Ade; Suryani, Dessy Rizki; Ruslau, Maria F. V.; Meirista, Etriana
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.36659

Abstract

The stability and equilibrium behavior of predator–prey systems involving cannibalistic interactions is crucial for explaining the long-term sustainability of ecological communities. This study aims to analyze the dynamics of a modified predator–prey model by incorporating cannibalism in predators as a self-regulating mechanism influencing population control. This study is a literature-based research, and the instruments employed are non-physical in nature, including a mathematical model, mathematical analysis tools, and numerical computation frameworks. The research methodology employs literature review and analysis of a model formulated as a system of nonlinear differential equations.  This system describes the population dynamics of two prey species and one predator species exhibiting cannibalistic tendencies. Analytical and numerical approaches are utilized to determine equilibrium points, evaluate local stability, and assess the effects of density-dependent mortality and cannibalistic behavior on ecosystem balance. The results show that the proposed predator–prey model admits one trivial equilibrium, five semi-trivial equilibrium, and one coexistence equilibrium. The coexistence equilibrium is locally asymptotically stable and satisfies the Routh–Hurwitz stability criterion. Simulation numeric the cannibalism parameter and density-dependent mortality rates play a significant role in stabilizing the predator population dynamics. When the mortality coefficient increases, the predator population decreases toward a lower equilibrium point, while the prey population slightly increases due to reduced predation pressure. Eigenvalue analysis reinforces these findings by confirming the system's compliance with the Routh–Hurwitz stability conditions. Ecological implications, these findings suggest that cannibalistic behavior in predators acts as a natural feedback mechanism to regulate population density, enhance ecosystem stability, and support the long-term sustainability of predator–prey interactions. The cannibalistic character of the predator species does not necessarily lead to species extinction, but can instead facilitate a sustainable and balanced coexistence within the ecosystem.
Co-Authors Doo, Katarina Clara Meirista, Etriana Nurhayati Nurhayati Pratama, Rian Ade Suryani, Dessy Rizki Untayana, Juliana R.