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All Journal Medicina CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Penelitian Pendidikan Matematika dan Sains SITEKIN: Jurnal Sains, Teknologi dan Industri E-Dimas: Jurnal Pengabdian kepada Masyarakat Didacticofrancia: Journal Didactique du FLE English and Literature Journal Jurnal EMT KITA BAREKENG: Jurnal Ilmu Matematika dan Terapan Communication in Biomathematical Sciences WAKTU: Jurnal Teknik UNIPA Martabe : Jurnal Pengabdian Kepada Masyarakat Jurnal Matematika UNAND Jurnal Abdi: Media Pengabdian Kepada Masyarakat Jambura Journal of Biomathematics (JJBM) MATHunesa: Jurnal Ilmiah Matematika Jurnal Pengabdian Masyarakat dan aplikasi Teknologi Franconesia Journal of French Teaching, Linguistics, Literature, and Culture Indonesian Journal of Computational and Applied Mathematics
DIAN SAVITRI
Department of Child Health, Udayana University Medical School/Sanglah Hospital Denpasar
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 Materials Science & Nanotechnology Mathematics Mechanical Engineering Medicine & Pharmacology Physics Social Sciences Transportation Other

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Stability Analysis and Invasion Thresholds in a Rosenzweig--MacArthur Model with Prey Immigration and Cooperative Hunting Faustin, Naufal Daffa; Savitri, Dian
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.v11i1.40677

Abstract

Predator--prey systems with multiple interacting ecological mechanisms require integrated modeling approaches for realistic analysis. This study develops a unified Rosenzweig--MacArthur model incorporating both continuous prey immigration and cooperative hunting among predators to analyze how these combined mechanisms affect equilibrium existence, stability, and transient dynamics. Analytical methods derive explicit invasion thresholds and local stability conditions through eigenvalue analysis, while numerical simulations with biologically plausible parameters compare two dynamical regimes: baseline conditions produce stable-node convergence, whereas high-efficiency conditions yield stable-spiral oscillations. Results show that immigration elevates prey density above invasion thresholds, enabling predator persistence, while increased cooperation intensity transitions the system from monotonic to oscillatory convergence. The integrated framework demonstrates how bottom-up (immigration) and top-down (cooperation) processes interact to shape predator--prey dynamics, providing testable predictions for ecosystems where both mechanisms operate simultaneously and establishing a foundation for more complex ecological modeling.
Stage-Structured Predator Model with Prey Protection: Application to Rice Plants–Leptocorisa oratorius Rahmah, Safira; Savitri, Dian
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.v11i1.40733

Abstract

This study investigates a stage-structured predator–prey model consisting of prey, juvenile predators, and adult predators. The prey population follows logistic growth, while predation is described using a Holling type I functional response. Prey protection is incorporated through a protection parameter (1-m), representing the proportion of prey that successfully avoid predation by reducing the predation rate of adult predators. The model is analyzed by determining equilibrium points and examining their existence and stability. The results show four equilibrium points: total population extinction, prey-only equilibrium, juvenile predator extinction, and coexistence equilibrium. Predator extinction occurs when predation efficiency and predator reproduction are insufficient to compensate for predator mortality, whereas coexistence occurs when predation and conversion rates exceed mortality thresholds. Numerical simulations support the analytical results and demonstrate that increasing prey protection reduces predation pressure and may lead to predator decline, while appropriate predation efficiency promotes stable coexistence. These findings highlight the ecological importance of prey defense mechanisms in predator–prey interactions, particularly in rice–Leptocorisa oratorius.
Stability and Bifurcation of a 3D Eco Epidemiological Predator Prey Model with Pesticide Savitri, Aqiila Ollyana; Savitri, Dian
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.
Dynamics of Predator-Prey Model with Holling Type II Involving Predator Stage-Structured and Cannibalism Sari, Sela Tri Indah; Savitri, Dian
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
Co-Authors ABADI Akmal Ali, Muhamad Restu Alya, Aiza Andreani, Phobe APRILIA, VERNANDA Beay, Lazarus Kalvein BUDI RAHADJENG Danu Erlangga, Muhammad Dewi, Mifta Kharisma Dina Kartika Maharani DINA KARTIKA MAHARANI Dini Kinati Fardah Dino, Awan Eghary, Nabila Kholifatul Yuniar Faradilla, Anisa' Faustin, Naufal Daffa Fitri, Davina Alma Gastriani, Ovi Prina Hamzah, Ahmad Taufik Hasan S. Panigoro Hidajati, Ninik Wahju I Made Kardana Isaloka, Ilo Jakfar, Muhammad Khofifah, Rike Farikha Kusumawati Dwiningsih Lydia Rohmawati Mahameru Rosy Rochmatullah Manuharawati Meladelvia, Nabilah Ni Putu Siadi Purniti Ninuk Lustyantie Nisa', Anastasya Choirun Phibeta, Toni Prawoto, Budi P. Putri, Laras Kinanti RADEN SULAIMAN Rahmah, Safira Rahmi, Emli Ratna Salsabila, An Nisa Salsabillah, Atiyah Safitri Sari, Sela Tri Indah Savitri, Aqiila Ollyana Sri Harini Ekowati Sri Mulyani Subur Ismail, Subur Thoriq, Abil Alfath Umaroh, Siti Zulfaniah Wiediartini Wiediartini