Dynamics of a predator-prey model with the Allee effect for the predator induced by weighted harvesting strategy

Jing Xu; Tao Zou; Jing Xu; Tao Zou

doi:10.3934/math.2026025

AIMS Mathematics

2026, Volume 11, Issue 1: 578-593. doi: 10.3934/math.2026025

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Research article

Dynamics of a predator-prey model with the Allee effect for the predator induced by weighted harvesting strategy

Jing Xu ^{1
,
,},
Tao Zou ²

1.
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: 08 October 2025 Revised: 14 December 2025 Accepted: 29 December 2025 Published: 08 January 2026
MSC : 92D25, 92D40

Over-exploitation of natural resources poses cascading challenges to the environment, economy, and public health. To mitigate these adverse impacts and achieve long-term ecological and socioeconomic balance, sustainable development strategies are imperative. Thus, in this paper, we developed a predator-prey model with state-dependent impulsive control, grounded in the weighted escapement policy, to regulate resource harvesting more realistically. We investigated the model's dynamical behaviors, focusing on the existence and stability of semi-trivial and order-1 periodic solutions. To enhance economic viability while ensuring sustainability, an optimization problem was formulated to maximize long-term profits via optimal harvesting schemes. Finally, numerical simulations validated the theoretical results, quantified the optimal harvesting level and weight parameter of the weighted escapement policy, and provided actionable insights for practical resource management.
- Allee effect,
- weighted harvesting strategy,
- periodic solution,
- orbital stability,
- optimization
Citation: Jing Xu, Tao Zou. Dynamics of a predator-prey model with the Allee effect for the predator induced by weighted harvesting strategy[J]. AIMS Mathematics, 2026, 11(1): 578-593. doi: 10.3934/math.2026025

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Abstract

Over-exploitation of natural resources poses cascading challenges to the environment, economy, and public health. To mitigate these adverse impacts and achieve long-term ecological and socioeconomic balance, sustainable development strategies are imperative. Thus, in this paper, we developed a predator-prey model with state-dependent impulsive control, grounded in the weighted escapement policy, to regulate resource harvesting more realistically. We investigated the model's dynamical behaviors, focusing on the existence and stability of semi-trivial and order-1 periodic solutions. To enhance economic viability while ensuring sustainability, an optimization problem was formulated to maximize long-term profits via optimal harvesting schemes. Finally, numerical simulations validated the theoretical results, quantified the optimal harvesting level and weight parameter of the weighted escapement policy, and provided actionable insights for practical resource management.

References

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