Resmawan Resmawan, Agus Suryanto, Isnani Darti, Hasan S. Panigoro
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. © 2025 Author(s).
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya Jln. Veteran No 10-11, Ketawanggede, Lowokwaru, Jawa Timur, Malang, 65145, Indonesia; Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Gorontalo, Jln. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Bone Bolango, Gorontalo, 96554, Indonesia
Research at a Glance
Register to unlock
Topics & SDG Alignment
Register to unlock
Collaboration
Register to unlock
Author Profile (Selected)
Register to unlock
References Overview
Register to unlock
Journal & Source
Register to unlock
Metadata & Integrity
Register to unlock