Dynamics of a modified Leslie–Gower model with dual Allee effects under unilateral and bilateral control

Jing Xu; Haoyang Shen; Xinyi Cao; Jing Xu; Haoyang Shen; Xinyi Cao

doi:10.3934/math.2026726

AIMS Mathematics

2026, Volume 11, Issue 6: 17820-17837. doi: 10.3934/math.2026726

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Research article

Dynamics of a modified Leslie–Gower model with dual Allee effects under unilateral and bilateral control

1.
Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
2.
School of Artificial Intelligence and Computer Science, Hubei Normal University, Huangshi 435002, China

Received: 18 April 2026 Revised: 26 May 2026 Accepted: 01 June 2026 Published: 18 June 2026
MSC : 92D25, 92D40

This paper establishes unilateral and bilateral impulsive control frameworks based on a modified Leslie–Gower model with dual Allee effects. The existence and orbital stability of order-1 and order-2 periodic solutions are proved by differential equation geometric theory. Numerical simulations are performed to validate the theoretical results, and bifurcation diagrams reveal parameter-dependent dynamical properties. Unilateral control can prevent prey extinction caused by the Allee effect or suppress excessive prey growth, thereby avoiding predator outbreaks and the resulting prey loss. In contrast, bilateral control precisely keeps prey and predator populations within reasonable ecological thresholds, and achieves stable population persistence as well as sustainable utilization of ecological resources.
- Allee effect,
- unilateral and bilateral control,
- successor function,
- periodic solution,
- stability
Citation: Jing Xu, Haoyang Shen, Xinyi Cao. Dynamics of a modified Leslie–Gower model with dual Allee effects under unilateral and bilateral control[J]. AIMS Mathematics, 2026, 11(6): 17820-17837. doi: 10.3934/math.2026726

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Abstract

This paper establishes unilateral and bilateral impulsive control frameworks based on a modified Leslie–Gower model with dual Allee effects. The existence and orbital stability of order-1 and order-2 periodic solutions are proved by differential equation geometric theory. Numerical simulations are performed to validate the theoretical results, and bifurcation diagrams reveal parameter-dependent dynamical properties. Unilateral control can prevent prey extinction caused by the Allee effect or suppress excessive prey growth, thereby avoiding predator outbreaks and the resulting prey loss. In contrast, bilateral control precisely keeps prey and predator populations within reasonable ecological thresholds, and achieves stable population persistence as well as sustainable utilization of ecological resources.

References

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