The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey

Chengchong Lu; Xinxin Liu; Zhicheng Li; Chengchong Lu; Xinxin Liu; Zhicheng Li

doi:10.3934/math.20231481

AIMS Mathematics

2023, Volume 8, Issue 12: 28897-28925. doi: 10.3934/math.20231481

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Research article

The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey

School of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou, China

Received: 24 July 2023 Revised: 07 October 2023 Accepted: 18 October 2023 Published: 25 October 2023
MSC : 34D23, 37N25, 92B05

The study of harvesting mechanisms in predator-prey systems with an Allee effect on prey has always garnered significant attention. In this paper, the dynamics and harvesting strategies of a predator-prey system are investigated, where the prey is subject to the Allee effect. The positivity and boundedness of solutions, the existence and stability of equilibria are further studied. The existence of a Hopf bifurcation at the interior equilibrium point of the system is investigated and verified by numerical simulations. Furthermore, we investigate the maximum sustainable yield (MSY), maximum sustainable total yield (MSTY) and the optimal economic profit of the proposed system. We find that MSY can be attained through predator harvesting, while MSTY is observed when harvesting efforts are uniform across species. In these situations, the biological system maintains stability. Using the method of control parametrization, the optimal economic profit and harvesting strategy are obtained. The results show that the harvesting efforts can affect the stability of the system, resulting in several interesting biological phenomena. This research provides a theoretical basis for biological resource management.
- predator-prey,
- Allee effect,
- hopf bifurcation,
- MSTY,
- optimal harvesting
Citation: Chengchong Lu, Xinxin Liu, Zhicheng Li. The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey[J]. AIMS Mathematics, 2023, 8(12): 28897-28925. doi: 10.3934/math.20231481

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Abstract

The study of harvesting mechanisms in predator-prey systems with an Allee effect on prey has always garnered significant attention. In this paper, the dynamics and harvesting strategies of a predator-prey system are investigated, where the prey is subject to the Allee effect. The positivity and boundedness of solutions, the existence and stability of equilibria are further studied. The existence of a Hopf bifurcation at the interior equilibrium point of the system is investigated and verified by numerical simulations. Furthermore, we investigate the maximum sustainable yield (MSY), maximum sustainable total yield (MSTY) and the optimal economic profit of the proposed system. We find that MSY can be attained through predator harvesting, while MSTY is observed when harvesting efforts are uniform across species. In these situations, the biological system maintains stability. Using the method of control parametrization, the optimal economic profit and harvesting strategy are obtained. The results show that the harvesting efforts can affect the stability of the system, resulting in several interesting biological phenomena. This research provides a theoretical basis for biological resource management.

References

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