Impact of double Allee effect on the dynamics and stability of a predator-prey model

Asifa Tassaddiq; Rizwan Ahmed; Jawad Khan; Youngmoon Lee; Asifa Tassaddiq; Rizwan Ahmed; Jawad Khan; Youngmoon Lee

doi:10.3934/math.2026048

AIMS Mathematics

2026, Volume 11, Issue 1: 1117-1144. doi: 10.3934/math.2026048

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Research article

Impact of double Allee effect on the dynamics and stability of a predator-prey model

1.
Department of Computer Science, College of Computer and Information Sciences, Majmaah University, Al Majmaah 11952, Saudi Arabia
2.
Department of Mathematics, Air University Multan Campus, Multan 60001, Pakistan
3.
School of Computing, Gachon University, Seongnam 13120, Republic of Korea
4.
Department of Robotics, Hanyang University, Ansan 15588, Republic of Korea
5.
Department of Applied AI, Hanyang University, Ansan 15588, Republic of Korea

Received: 10 October 2025 Revised: 27 November 2025 Accepted: 02 December 2025 Published: 15 January 2026
MSC : 39A28, 39A30

In this paper, we investigated the complex dynamics of a discrete-time predator-prey model incorporating a double Allee effect in the prey population. We investigated the existence and stability of biologically meaningful fixed points, including extinction, prey-only, and coexistence equilibria. Through analytical and numerical bifurcation analysis, we demonstrated that the model underwent a Neimark-Sacker bifurcation as key parameters varied, leading to quasi-periodic oscillations that characterized realistic population cycles. Our results revealed that stronger Allee effects tend to destabilize the model, increasing extinction risks and promoting oscillatory dynamics, while higher predator mortality rates and saturation in predation response enhance stability. A comparative analysis with models lacking the Allee effect highlights its critical role in delaying equilibrium convergence and inducing instability at low population densities. These findings provide important insights for ecological conservation, particularly for species vulnerable to population depletion, and contribute to the theoretical understanding of predator-prey models with density-dependent growth constraints.
- predator-prey model,
- Allee effect,
- stability,
- bifurcation
Citation: Asifa Tassaddiq, Rizwan Ahmed, Jawad Khan, Youngmoon Lee. Impact of double Allee effect on the dynamics and stability of a predator-prey model[J]. AIMS Mathematics, 2026, 11(1): 1117-1144. doi: 10.3934/math.2026048

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Abstract

In this paper, we investigated the complex dynamics of a discrete-time predator-prey model incorporating a double Allee effect in the prey population. We investigated the existence and stability of biologically meaningful fixed points, including extinction, prey-only, and coexistence equilibria. Through analytical and numerical bifurcation analysis, we demonstrated that the model underwent a Neimark-Sacker bifurcation as key parameters varied, leading to quasi-periodic oscillations that characterized realistic population cycles. Our results revealed that stronger Allee effects tend to destabilize the model, increasing extinction risks and promoting oscillatory dynamics, while higher predator mortality rates and saturation in predation response enhance stability. A comparative analysis with models lacking the Allee effect highlights its critical role in delaying equilibrium convergence and inducing instability at low population densities. These findings provide important insights for ecological conservation, particularly for species vulnerable to population depletion, and contribute to the theoretical understanding of predator-prey models with density-dependent growth constraints.

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