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Optimal impulsive harvesting policies for single-species populations

Author

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  • Dou, Jiawei
  • Li, Shundong

Abstract

In this paper, we address an optimal impulsive control problem with the aim of optimizing the harvesting rate for a non-autonomous logistic model. In addressing this problem, we combine bang–bang and singular controls for an impulsive optimization problem in which the singular controls are blocked at certain harvesting times. In our approach, we first obtain the singular controls by applying a Pontryagin optimal control framework for impulsive systems. Second, we investigate and derive a number of relationships characterizing the optimal harvesting rates and present an optimization principle: the optimal path lies as close as possible to the singular path. Finally, based on this optimization principle, we obtain analytical expressions for the optimal harvesting policy for our problem and use numerical simulations to demonstrate the effectiveness of our method. This study develops concepts and theory related to continuous control problems and applies them to impulsive control problems, and extends the related work of Xiao et al. (2006) and Braverman and Mamdani (2008).

Suggested Citation

  • Dou, Jiawei & Li, Shundong, 2017. "Optimal impulsive harvesting policies for single-species populations," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 145-155.
    • Handle: RePEc:eee:apmaco:v:292:y:2017:i:c:p:145-155
    DOI: 10.1016/j.amc.2016.07.027
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    Citations

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    Cited by:

    1. Zuxiong Li & Shengnan Fu & Huili Xiang & Hailing Wang, 2021. "Qualitative Analysis of a Single-Species Model with Distributed Delay and Nonlinear Harvest," Mathematics, MDPI, vol. 9(20), pages 1-26, October.
    2. Jang, Geunsoo & Cho, Giphil, 2022. "Optimal harvest strategy based on a discrete age-structured model with monthly fishing effort for chub mackerel, Scomber japonicus, in South Korea," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    3. Tian, Yuan & Li, Huanmeng & Sun, Kaibiao, 2024. "Complex dynamics of a fishery model: Impact of the triple effects of fear, cooperative hunting and intermittent harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 31-48.

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