Complex dynamics of a predator-prey fishery model: The impact of the Allee effect and bilateral intervention

Yuan Tian; Yang Liu; Kaibiao Sun; Yuan Tian; Yang Liu; Kaibiao Sun

doi:10.3934/era.2024297

Electronic Research Archive

2024, Volume 32, Issue 11: 6379-6404. doi: 10.3934/era.2024297

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Research article

Complex dynamics of a predator-prey fishery model: The impact of the Allee effect and bilateral intervention

Yuan Tian ^{1
,
,},
Yang Liu ¹,
Kaibiao Sun ^{2
,
,}

1.
School of Science, Dalian Maritime University, Dalian 116026, China
2.
School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China

Received: 02 September 2024 Revised: 12 November 2024 Accepted: 15 November 2024 Published: 22 November 2024

The Allee effect is an important mechanism in ecosystems and a realistic description of the interaction between species. The study of the predator-prey model with the Allee effect is of great significance to promote the development of marine ecology. In this work, three aspects of studies are presented: Modelling and analysis: a predator-prey fishery model with the Allee effect in prey and generalist predator is first established. The existence, type, and stability of the boundary equilibria as well as the number of interior equilibria of the proposed model are discussed. Parameter influence: the bifurcations in the predation system are analyzed by selecting the capture rate of prey by the predator and Allee threshold as key parameters, and the results show that the system will undergo saddle-node bifurcation and Bogdanov-Takens bifurcation of codimension at least 2 and 3. Control measures: a bilateral intervention strategy is adopted for the capture and protection of marine fish. The existence and stability of the order-1 periodic solution and the order-2 periodic solution of the control system are analyzed by using the differential equation geometry theory. Additionally, numerical simulations are carried out to verify the correctness of the conclusions, and illustrate the impact of the Allee effect and bilateral intervention on the ecosystem, which provides an effective method for modern fishery conservation and harvesting.
- Allee effect,
- bilateral control,
- Bogdanov-Takens bifurcation,
- periodic solution,
- saddle-node bifurcation
Citation: Yuan Tian, Yang Liu, Kaibiao Sun. Complex dynamics of a predator-prey fishery model: The impact of the Allee effect and bilateral intervention[J]. Electronic Research Archive, 2024, 32(11): 6379-6404. doi: 10.3934/era.2024297

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Abstract

The Allee effect is an important mechanism in ecosystems and a realistic description of the interaction between species. The study of the predator-prey model with the Allee effect is of great significance to promote the development of marine ecology. In this work, three aspects of studies are presented: Modelling and analysis: a predator-prey fishery model with the Allee effect in prey and generalist predator is first established. The existence, type, and stability of the boundary equilibria as well as the number of interior equilibria of the proposed model are discussed. Parameter influence: the bifurcations in the predation system are analyzed by selecting the capture rate of prey by the predator and Allee threshold as key parameters, and the results show that the system will undergo saddle-node bifurcation and Bogdanov-Takens bifurcation of codimension at least 2 and 3. Control measures: a bilateral intervention strategy is adopted for the capture and protection of marine fish. The existence and stability of the order-1 periodic solution and the order-2 periodic solution of the control system are analyzed by using the differential equation geometry theory. Additionally, numerical simulations are carried out to verify the correctness of the conclusions, and illustrate the impact of the Allee effect and bilateral intervention on the ecosystem, which provides an effective method for modern fishery conservation and harvesting.

References

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