BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application

DYNAMICS OF A PREY-PREDATOR MODEL WITH ALLEE EFFECTS AND HOLLING TYPE IV FUNCTIONAL RESPONSE: LOCAL STABILITY AND NUMERICAL EXPLORATION OF BIFURCATIONS

Resmawan, Resmawan (Unknown)
Suryanto, Agus (Unknown)
Darti, Isnani (Unknown)
Panigoro, Hasan S. (Unknown)



Article Info

Publish Date
01 Sep 2025

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.

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Journal Info

Abbrev

barekeng

Publisher

Subject

Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

Description

BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure ...