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A dynamical analysis of a predator-prey model: Exploring the influence of the Allee effect, environmental protection, and supplementary food sources
Jambura Journal of Biomathematics (JJBM) · Vol. ume (2025) · hlm. 311–328
- ISSN
- 2723-0317
- Terbit
- 2025-12-03
- Penerbit
- Department of Mathematics, Universitas Negeri Gorontalo
- Bahasa
- eng
Abstrak
This paper introduces a new predator-prey model with supplementary food sorces for the predator and the Allee effect on prey. Analytical proof of the existence, uniqueness, non-negativity, and boundedness of the solutions validates the model. Three equilibrium points are found: a trivial point, whose local stability depends on the Allee effect’s strength; a semi-trivial point, and an interior point whose local stability depends on certain conditions. The Lyapunov function and La Salle invariance principle show that each equilibrium point is globally asymptotically stable. The system displays intricate dynamical behaviors, including forward and Hopf bifurcations, along with bistability, which is regulated by critical parameters such as the predation conversion rate, environmental protection rate, and supplementary food sources. Under a weak Allee effect, increasing the predation conversion rate or supplementary food can shift the system from predator extinction to oscillatory coexistence. In contrast, under a strong Allee effect, these increases may instead drive both species to extinction if thresholds are exceeded. Moreover, variations in environmental protection rate yield contrasting outcomes: while a higher rate under weak Allee conditions may stabilize prey and eliminate predators, under strong Allee conditions, it may lead to total extinction. These findings illustrate the intricate relationship between biological and environmental components, highlighting the necessity for preventive measures and supplementary resources in population outcomes. The findings indicate that environmental protection and supplementary food sources influence species persistence and extinction in predator-prey dynamics, which is crucial for ecological conservation.
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- State University of Gorontalo
- University of Brawijaya
- Universitas Negeri Surabaya
- Universitas Trunodjoyo Madura
- Sebelas Maret University
- University of Technology Malaysia
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Tampilkan sebagai tabel
| Rekan penulis | Organisasi | Artikel bersama |
|---|---|---|
| Emli Rahmi | State University of Gorontalo | 8 |
| Lailany Yahya | State University of Gorontalo | 6 |
| Trisilowati Trisilowati | University of Brawijaya | 6 |
| Agusyarif Rezka Nuha | State University of Gorontalo | 5 |
| Wuryansari Muharini Kusumawinahyu | University of Brawijaya | 5 |
| Dian Savitri | Universitas Negeri Surabaya | 4 |
| Raqqasyi Rahmatullah Musafir | University of Brawijaya | 4 |
| Sri Lestari Mahmud | State University of Gorontalo | 3 |
| Ach. Khozaimi | Universitas Trunodjoyo Madura | 2 |
| Onik Febria Damayanti | University of Brawijaya | 2 |
| Novianita Achmad | State University of Gorontalo | 2 |
| Lanto Ningrayati Amali | State University of Gorontalo | 1 |
| Femy Mahmud Sahami | State University of Gorontalo | 1 |
| Harto S. Malik | State University of Gorontalo | 1 |
| Sitawati | Afiliasi tidak diketahui | 1 |
| Arifin Noor | Afiliasi tidak diketahui | 1 |
| Euis Elih Nurlaelih | Afiliasi tidak diketahui | 1 |
| D. R. R. Damaiyanti | University of Brawijaya | 1 |
| Nurwan Nurwan | State University of Gorontalo | 1 |
| Moh Rizal Husain | State University of Gorontalo | 1 |
| Isran R Olii | State University of Gorontalo | 1 |
| Nur Safitri Abdul | State University of Gorontalo | 1 |
| Nazrilla Hasan Laita | State University of Gorontalo | 1 |
| Asriadi Asriadi | State University of Gorontalo | 1 |
| Annisa Maharani Brahim | State University of Gorontalo | 1 |
| Dewi Rahmawaty Isa | State University of Gorontalo | 1 |
| La Ode Nashar | State University of Gorontalo | 1 |
| Amanda Adityaningrum | State University of Gorontalo | 1 |
| Suci Astutik | University of Brawijaya | 1 |
| Darmanto Darmanto | Sebelas Maret University | 1 |
| Nurjannah Nurjannah | University of Brawijaya | 1 |
| Diego Irsandy | University of Brawijaya | 1 |
| Muhammad Hisyam Lee | University of Technology Malaysia | 1 |
| Rismania Hartanti Putri Yulianing Damayanti | University of Brawijaya | 1 |
| Marsudi Marsudi | University of Brawijaya | 1 |
| Syaiful Anam | University of Brawijaya | 1 |
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