Open access Journal SINTA 3
DYNAMICS OF A PREY-PREDATOR MODEL WITH ALLEE EFFECTS AND HOLLING TYPE IV FUNCTIONAL RESPONSE: LOCAL STABILITY AND NUMERICAL EXPLORATION OF BIFURCATIONS
BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 19 No. 4 (2025) · pp. 2891–2906
- ISSN
- 2615-3017, 1978-7227
- Published
- 2025-09-01
- Publisher
- PATTIMURA UNIVERSITY
- Language
- eng
Abstract
This study presents a prey-predator model incorporating the Allee effect and Holling Type IV Functional Response. The model identifies three equilibrium points: the zero-equilibrium, the predator extinction equilibrium, and the positive equilibrium. Under specific conditions, all these points exhibit local asymptotic stability. The Allee effect is an important factor in determining the stability of the equilibrium point. A weak Allee effect can destabilize the zero-equilibrium point, while a strong Allee effect ensures its local asymptotic stability, potentially leading to the extinction of both species. Additionally, forward and Hopf bifurcation under weak Allee conditions occur at the predator extinction equilibrium point. In contrast, a strong Allee effect may cause bistability between the zero-equilibrium and predator extinction equilibrium points. This evidence suggests that prey can survive without predators; however, a strong Allee effect might result in prey extinction if the population decreases significantly. The Holling Type IV functional response illustrates the impact of prey group defense, which diminishes predation pressure as prey density increases, thereby facilitating the development of limit cycles and establishing a positive equilibrium under specific parameter conditions. This mechanism is crucial for managing predator-prey cohabitation and influencing the system's bifurcation structure. The final section of the study includes numerical simulations to support the analytical findings. The interplay between the Allee effect and the Holling Type IV functional response yields complex dynamics, encompassing bistability, oscillation behavior, and sensitivity to initial conditions. Their collaborative interaction amplifies the system's nonlinearity, enabling the creation of various dynamic behaviors that are extremely sensitive to fluctuations in parameter values.
Collaboration network of the authors
40 authors · 113 co-authorship links · 16 across different organisations · showing the 40 most connected
Hover or tap a name to highlight its co-authors. Double-click to open the author's page.
- State University of Gorontalo
- University of Brawijaya
- State University of Semarang
- University of Technology Malaysia
- Affiliation unknown
- Different organisations
- Same organisation
- Affiliation unknown
- Thicker line = more joint articles · bigger circle = more articles
Show as table
| Co-author | Organisation | Joint articles |
|---|---|---|
| Agus Suryanto | State University of Semarang | 11 |
| Emli Rahmi | State University of Gorontalo | 8 |
| Lailany Yahya | State University of Gorontalo | 6 |
| Agusyarif Rezka Nuha | State University of Gorontalo | 5 |
| Dian Savitri | Affiliation unknown | 4 |
| Trisilowati Trisilowati | University of Brawijaya | 3 |
| Sri Lestari Mahmud | State University of Gorontalo | 3 |
| Raqqasyi Rahmatullah Musafir | 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 | Affiliation unknown | 1 |
| Arifin Noor | Affiliation unknown | 1 |
| Euis Elih Nurlaelih | Affiliation unknown | 1 |
| D. R. R. Damaiyanti | Affiliation unknown | 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 | University of Brawijaya | 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 |
| Ach. Khozaimi | University of Brawijaya | 1 |
| Wuryansari Muharini Kusumawinahyu | University of Brawijaya | 1 |
Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.