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All Journal International Journal of Evaluation and Research in Education (IJERE) CAUCHY: Jurnal Matematika Murni dan Aplikasi E-Dimas: Jurnal Pengabdian kepada Masyarakat Jurnal Manajemen Aset Infrastruktur dan Fasilitas WAKTU: Jurnal Teknik UNIPA Martabe : Jurnal Pengabdian Kepada Masyarakat J-ADIMAS (Jurnal Pengabdian kepada Masyarakat) JPPIPA (Jurnal Penelitian Pendidikan IPA) Jurnal Abdi: Media Pengabdian Kepada Masyarakat Jambura Journal of Biomathematics (JJBM) Community Empowerment MATHunesa: Jurnal Ilmiah Matematika Abdimas Altruis: Jurnal Pengabdian Kepada Masyarakat
Dian Savitri
Departemen Matematika, Universitas Negeri Surabaya, Surabaya.
Agriculture, Biological Sciences & Forestry Arts Humanities Chemical Engineering, Chemistry & Bioengineering Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Environmental Science Industrial & Manufacturing Engineering Languange, Linguistic, Communication & Media Library & Information Science Materials Science & Nanotechnology Mathematics Mechanical Engineering Public Health Social Sciences Transportation Other

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PELATIHAN PEMBUATAN PERANGKAT PEMBELAJARAN KURIKULUM MERDEKA BERBASIS PROJECT BASED LEARNING (PjBL) BAGI GURU SMA PONDOK PESANTREN BAYT AL-HIKMAH Kusumawati Dwiningsih; Dina Kartika Maharani; Dian Savitri; Aiza Alya; Ilo Isaloka; Muhammad Danu Erlangga
Martabe : Jurnal Pengabdian Kepada Masyarakat Vol 6, No 6 (2023): martabe : jurnal pengabdian kepada masyarakat
Publisher : Universitas Muhammadiyah Tapanuli Selatan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31604/jpm.v6i6.1920-1933

Abstract

Kurangnya ketersediaan dan rendahnya kemampuan guru untuk menyusun Perangkat Pembelajaran Berorientasi Project Based Learning (PjBL) dan Berbasis Kurikulum Merdeka sebagai sumber belajar peserta didik di masa pemulihan pembelajaran pasca pandemi yang menyebabkan kemauan peserta didik untuk belajar mengalami penurunan, peserta didik tidak bersungguh-sungguh dalam belajar karena terbiasa menggunakan internet sebagai sumber belajar. Program yang dapat dijalankan dengan guru yang tergabung dalam Guru SMA Pondok Pesantren Bayt Al Hikmah sebagai mitra dan tim pelaksana PPM–PKM adalah perlunya peningkatan kompetensi guru terhadap pemahaman, keterampilan, dan kecakapan dalam menyusun perangkat pembelajaran kurikulum merdeka. Metode yang digunakan pada pengabdian ini meliputi 1) Persiapan, 2) Penulisan, 3) Pelaksanaan Pelatihan, 4) Tahap Monitoring dan Evaluasi, dan 5) Publikasi. Kegiatan ini memiliki target yang ingin dicapai yaitu meningkatnya kemampuan guru dalam menyusun perangkat pembelajaran yang Berorientasi Project Based Learning (PjBL) dan Berbasis Kurikulum Merdeka. Indikator keberhasilan kegiatan ini meliputi 1) Penugasan Pembuatan Perangkat, 2) Hasil Angket Respon, 3) Tingkat Kehadiran Peserta, dan 4) Kelengkapan Penugasan.
Stability Analysis of a Predator-Prey Model with Disease in Prey, Predator Harvesting, and Internal Migration of Susceptible Prey in a Closed Ecosystem Muhammad Thariq Firmansyah; Dian Savitri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41546

Abstract

This study develops and analyzes a mathematical model of a predator-prey system incorporating three simultaneous ecological factors: disease in the prey population, harvesting of the predator, and internal migration of healthy prey within a closed ecosystem. The prey population is divided into two compartments healthy prey and infected prey where disease transmission follows the law of mass action. The predator population is subject to a constant harvesting rate representing external pressure such as hunting or capture. Internal migration of healthy prey is modeled as a density-dependent flux governed by a migration parameter m, which drives the redistribution of healthy prey across spatial patches without allowing permanent emigration from the system. The model is formulated as a system of three autonomous ordinary differential equations. Six equilibrium points are identified, representing a range of ecological scenarios from total extinction to full coexistence of all populations. The local stability of each equilibrium point is analyzed by linearization via the Jacobian matrix, and stability conditions are derived in terms of the model parameters, including the application of the Routh–Hurwitz criterion for the coexistence equilibrium. A key finding is that the migration parameter m does not alter the location of equilibrium points but directly influences the eigenvalues of the Jacobian, thereby affecting the rate at which the system recovers from perturbations. Numerical simulations are conducted to verify and illustrate the analytical results. This work extends the model of Mansur et al. [1] by introducing an internal spatial dimension, offering a more ecologically realistic framework for understanding population dynamics in ecosystems where disease, harvesting, and migration co-occur
Dynamics of Predator-Prey Model with Holling Type II Involving Predator Stage-Structured and Cannibalism Sela Tri Indah Sari; Dian Savitri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41044

Abstract

Predator–prey models with nonlinear functional responses provide a robust framework for understanding population regulation and oscillatory dynamics. This study analyzes a three-dimensional predator–prey model incorporating Holling type II functional responses, explicit predator stage structure, and cannibalism. The primary objective is to investigate how adult predation, maturation, and cannibalism parameters influence equilibrium stability and the emergence of oscillations through Hopf bifurcation. Analytical results establish the existence and local stability of a positive coexistence equilibrium. For a biologically relevant parameter set, numerical simulations demonstrate that trajectories converge to the coexistence equilibrium (59.9078, 23.9092, 56.0552). This state is locally asymptotically stable, as the real parts of all Jacobian eigenvalues are negative. Numerical continuation methods are employed to detect Hopf bifurcations induced by key parameters. Two Hopf points are identified for the adult predation rate at 0.4211 and 8.7725, while the maturation rate induces bifurcations at 0.2661 and 0.5271. Additionally, the cannibalism parameter triggers a Hopf bifurcation at 0.1835, initiating periodic population oscillations. These results demonstrate that maturation and cannibalism define distinct instability thresholds, jointly governing the transition from stable coexistence to sustained oscillatory dynamics in stage-structured systems
Local Stability and Bifurcation Analysis of a Mangrove Detritus Small-Fish Model with Dynamic Harvesting Effort under a Beddington-DeAngelis Functional Response Donna Kurniasih; Dian Savitri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41486

Abstract

This study develops a three-dimensional mangrove detritus small fish model with a dynamics harvesting effort governed by a threshold rule and a Beddington DeAngelis functional response. The main objective is to understand how adaptive harvesting and consumer interference shape long-term dynamics and stability. Equilibrium points are derived and their local stability is examined using the Jacobian matrix and eigenvalue-based criteria, supported by numerical simulations. Bifurcation analysis with respect to the threshold parameter is performed using numerical continuation to detect qualitative transitions in system behavior. The results show the existence of biologically feasible coexistence equilibria with active harvesting, including a stable branch and an unstable branch. A Hopf bifurcation is detected at approximately a = 6.6159, confirming the emergence of sustained oscillations limit cycles in fish density and harvesting effort, while a fold limit point occurs near a = 22.001, indicating changes in equilibrium structure. Moreover, simulation scenarios demonstrate that reducing environmental capacity and increasing fish mortality can drive the system toward a no-effort equilibrium where harvesting collapses. These findings highlight the threshold parameter as a key control factor that can switch the system between stable harvesting, effort extinction, and oscillatory harvesting regimes.
Dynamical Analysis of a Trophic Model on Guano, Invertebrates, and Fish in Cave Ecosystems M Niko Axsella Ibrahim; Dian Savitri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41524

Abstract

This study investigates the dynamical interaction between guano biomass density (x), invertebrate biomass density (y), and fish biomass density (z) through a three-compartment trophic model representing a nutrient-based cave ecosystem. The analysis identifies three equilibrium points: the consumer-free equilibrium E0, the predator-free equilibrium E1, and the coexistence equilibrium E2. Local stability analysis shows that the coexistence equilibrium is asymptotically stable, characterized by eigenvalues with negative real parts (1 = -0.519706 and 2,3 = -0.085385 0.188169i). Numerical simulations using the fourth–fifth order Runge–Kutta method (RK45) support these analytical results, showing trajectories that exhibit damped oscillations before converging to the steady state. Furthermore, a bifurcation analysis reveals a critical Branching Point (BP) at the predation rate b2 0.043956. This threshold signifies a transcritical bifurcation where the system transitions from a predator-extinction regime to a stable coexistence regime, highlighting the sensitivity of the food web to energy transfer efficiency. These findings suggest that under the assumed parameter set, the interaction between guano nutrients, invertebrates, and fish can maintain a stable ecological balance through top-down control and nutrient-dependent dynamics.
Stability and Bifurcation of a 3D Eco Epidemiological Predator Prey Model with Pesticide Aqiila Ollyana Savitri; Dian Savitri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40676

Abstract

Eco--epidemiological predator--prey models provide an important mathematical framework for understanding the interaction between disease transmission, predation, and human intervention in ecological systems. This study investigates a three--dimensional deterministic model incorporating saturated disease incidence, Holling type II predation, and pesticide application. Analytical techniques are employed to determine the existence and local stability of biologically feasible equilibrium points, while numerical simulations using a fourth--order Runge--Kutta method illustrate the dynamical behavior of the system under different parameter regimes. The analysis reveals the possibility of disease--free, predator--free, and interior coexistence equilibria, as well as bistability depending on parameter values and initial conditions. Bifurcation analysis identifies critical thresholds in disease transmission and predator conversion efficiency that govern transitions between predator persistence and extinction. These findings provide theoretical insights for integrated pest management strategies by emphasizing the balance between chemical control and ecological stability.
Co-Authors Abadi Abadi Abadi Abadi Aiza Alya Ajeng Pramesti Putri Alicia Dhea Amara Aqiila Ollyana Savitri Bagas Saputra Bagas Saputra Bertha Yonata Budi P. Prawoto Budi Priyo Prawoto BUDI RAHADJENG Chih-Hsiung Ku Defi Ayunda Difitri Amalia Dina Kartika Maharani Dina Kartika Maharani Dini Kinati Fardah Donna Kurniasih Dwi Kristiatuti Suwardiah Elok Suidibyo Erman Erman Fadhilatun Ni’mah Farida Chasanah Guntur Trimulyono Hasan S. Panigoro Husni Mubarok Ilo Isaloka Jakfar, Muhammad Kevin Alifviansyah Kusumawati Dwiningsih Lydia Rohmawati M Niko Axsella Ibrahim Manuharawati Maya Dany Puspitasari Muhammad Danu Erlangga Muhammad Thariq Firmansyah Nadi Suprapto Nugrahani primary putri Nur Laili Af'idah Qurrotul Aini Raden Sulaiman Rahma Nurisnaini Rinie Pratiwi Puspitawati Rudianto Artiono Rudianto Artiono Ruli Rahmawati Ruli Rahmawati Sela Tri Indah Sari Sukarmin Sukarmin Toni Phibeta Wahyu Budi Sabtiawan