Stochastic modelling and analysis of harvesting model: Application to 'summer fishing moratorium' by intermittent control

Xiaoling Zou; Yuting Zheng

doi:10.3934/dcdsb.2020332

Article Contents

2021, Volume 26, Issue 9: 5047-5066. Doi: 10.3934/dcdsb.2020332

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Stochastic modelling and analysis of harvesting model: Application to "summer fishing moratorium" by intermittent control

Xiaoling Zou^1, , and
Yuting Zheng^2,

1.
Department of Mathematics, Harbin Institute of Technology(Weihai), Weihai 264209, China
2.
Department of Basic Course, Xingtai Polytechnic College, Xingtai 054000, China

^* Corresponding author: Xiaoling Zou
^* Corresponding author: Xiaoling Zou

Received: November 2019

Revised: June 2020

Early access: November 2020

Published: September 2021

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Abstract

As we all know, "summer fishing moratorium" is an internationally recognized management measure of fishery, which can protect stock of fish and promote the balance of marine ecology. In this paper, "intermittent control" is used to simulate this management strategy, which is the first attempt in theoretical analysis and the intermittence fits perfectly the moratorium. As an application, a stochastic two-prey one-predator Lotka-Volterra model with intermittent capture is considered. Modeling ideas and analytical skills in this paper can also be used to other stochastic models. In order to deal with intermittent capture in stochastic model, a new time-averaged objective function is proposed. Besides, the corresponding optimal harvesting strategies are obtained by using the equivalent method (equivalency between time-average and expectation). Theoretical results show that intermittent capture can affect the optimal harvesting effort, but it cannot change the corresponding optimal time-averaged yield, which are accord with observations. Finally, the results are illustrated by practical examples of marine fisheries and numerical simulations.

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Mathematics Subject Classification: Primary: 34F05, 93E03; Secondary: 60H10.

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Figure 1. Numerical simulations for sample paths

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Figure 2. Numerical simulations for time average

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Figure 3. The effects of intermittent control in one-dimensional situation

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