Bifurcation analysis and optimal control of a delayed single-species fishery economic model

Xin Gao; Yue Zhang; Xin Gao; Yue Zhang

doi:10.3934/mbe.2022378

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 8: 8081-8106. doi: 10.3934/mbe.2022378

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Research article

Bifurcation analysis and optimal control of a delayed single-species fishery economic model

Xin Gao ,
Yue Zhang ^,

College of Sciences, Northeastern University, Shenyang 110004, China

Academic Editor: Zhongwei Shen

Received: 02 March 2022 Revised: 10 May 2022 Accepted: 17 May 2022 Published: 06 June 2022

In this paper, a single-species fishery economic model with two time delays is investigated. The system is shown to be locally stable around the interior equilibrium when the parameters are in a specific range, and the Hopf bifurcation is shown occur as the time delays cross the critical values. Then the direction of Hopf bifurcation and the stability of bifurcated periodic solutions are discussed. In addition, the optimal cost strategy is obtained to maximize the net profit and minimize the waste by hoarding for speculation. We also design controls to minimize the waste by hoarding for the speculation of the system with time delays. The existence of the optimal controls and derivation from the optimality conditions are discussed. The validity of the theoretical results are shown via numerical simulation.
- fishery economic model,
- time delays,
- Hopf bifurcation,
- optimal control
Citation: Xin Gao, Yue Zhang. Bifurcation analysis and optimal control of a delayed single-species fishery economic model[J]. Mathematical Biosciences and Engineering, 2022, 19(8): 8081-8106. doi: 10.3934/mbe.2022378

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Abstract

In this paper, a single-species fishery economic model with two time delays is investigated. The system is shown to be locally stable around the interior equilibrium when the parameters are in a specific range, and the Hopf bifurcation is shown occur as the time delays cross the critical values. Then the direction of Hopf bifurcation and the stability of bifurcated periodic solutions are discussed. In addition, the optimal cost strategy is obtained to maximize the net profit and minimize the waste by hoarding for speculation. We also design controls to minimize the waste by hoarding for the speculation of the system with time delays. The existence of the optimal controls and derivation from the optimality conditions are discussed. The validity of the theoretical results are shown via numerical simulation.

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