A fishery predator-prey model with anti-predator behavior and complex dynamics induced by weighted fishing strategies

Yuan Tian; Yan Gao; Kaibiao Sun; Yuan Tian; Yan Gao; Kaibiao Sun

doi:10.3934/mbe.2023071

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 1558-1579. doi: 10.3934/mbe.2023071

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Research article

A fishery predator-prey model with anti-predator behavior and complex dynamics induced by weighted fishing strategies

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: 13 September 2022 Revised: 19 October 2022 Accepted: 27 October 2022 Published: 03 November 2022

In this work, a fishery predator-prey model with anti-predator behavior is presented according to the anti-predator phenomenon in nature. On the basis of this model, a capture model guided by a discontinuous weighted fishing strategy is established. For the continuous model, it analyzes how anti-predator behavior affects system dynamics. On this basis, it discusses the complex dynamics (order-$ m $ periodic solution ($ m = 1, 2 $)) induced by a weighted fishing strategy. Besides, in order to find the capture strategy that maximizes the economic profit in the fishing process, this paper constructs an optimization problem based on the periodic solution of the system. Finally, all of the results of this study have been verified numerically in MATLAB simulation.
- periodic solution,
- weighted fishing strategy,
- anti-predator behavior,
- optimization
Citation: Yuan Tian, Yan Gao, Kaibiao Sun. A fishery predator-prey model with anti-predator behavior and complex dynamics induced by weighted fishing strategies[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 1558-1579. doi: 10.3934/mbe.2023071

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Abstract

In this work, a fishery predator-prey model with anti-predator behavior is presented according to the anti-predator phenomenon in nature. On the basis of this model, a capture model guided by a discontinuous weighted fishing strategy is established. For the continuous model, it analyzes how anti-predator behavior affects system dynamics. On this basis, it discusses the complex dynamics (order-$ m $ periodic solution ($ m = 1, 2 $)) induced by a weighted fishing strategy. Besides, in order to find the capture strategy that maximizes the economic profit in the fishing process, this paper constructs an optimization problem based on the periodic solution of the system. Finally, all of the results of this study have been verified numerically in MATLAB simulation.

References

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