The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy

In presence of predator population, the prey population may significantly change their behavior. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. In this study, we propose a predator-prey fishery model i...

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Main Authors: Y. Tian, H. M. Li
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2022/9496599
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author Y. Tian
H. M. Li
author_facet Y. Tian
H. M. Li
author_sort Y. Tian
collection DOAJ
description In presence of predator population, the prey population may significantly change their behavior. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. In this study, we propose a predator-prey fishery model introducing the cost of fear into prey reproduction with Holling type-II functional response and prey-dependent harvesting and investigate the global dynamics of the proposed model. For the system without harvest, it is shown that the level of fear may alter the stability of the positive equilibrium, and an expression of fear critical level is characterized. For the harvest system, the existence of the semitrivial order-1 periodic solution and positive order-q (q≥1) periodic solution is discussed by the construction of a Poincaré map on the phase set, and the threshold conditions are given, which can not only transform state-dependent harvesting into a cycle one but also provide a possibility to determine the harvest frequency. In addition, to ensure a certain robustness of the adopted harvest policy, the threshold condition for the stability of the order-q periodic solution is given. Meanwhile, to achieve a good economic profit, an optimization problem is formulated and the optimum harvest level is obtained. Mathematical findings have been validated in numerical simulation by MATLAB. Different effects of different harvest levels and different fear levels have been demonstrated by depicting figures in numerical simulation using MATLAB.
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spelling doaj-art-fada0ff9eeb140b2b2af0f57b8a34a352025-02-03T01:04:31ZengWileyComplexity1099-05262022-01-01202210.1155/2022/9496599The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting StrategyY. Tian0H. M. Li1School of ScienceSchool of ScienceIn presence of predator population, the prey population may significantly change their behavior. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. In this study, we propose a predator-prey fishery model introducing the cost of fear into prey reproduction with Holling type-II functional response and prey-dependent harvesting and investigate the global dynamics of the proposed model. For the system without harvest, it is shown that the level of fear may alter the stability of the positive equilibrium, and an expression of fear critical level is characterized. For the harvest system, the existence of the semitrivial order-1 periodic solution and positive order-q (q≥1) periodic solution is discussed by the construction of a Poincaré map on the phase set, and the threshold conditions are given, which can not only transform state-dependent harvesting into a cycle one but also provide a possibility to determine the harvest frequency. In addition, to ensure a certain robustness of the adopted harvest policy, the threshold condition for the stability of the order-q periodic solution is given. Meanwhile, to achieve a good economic profit, an optimization problem is formulated and the optimum harvest level is obtained. Mathematical findings have been validated in numerical simulation by MATLAB. Different effects of different harvest levels and different fear levels have been demonstrated by depicting figures in numerical simulation using MATLAB.http://dx.doi.org/10.1155/2022/9496599
spellingShingle Y. Tian
H. M. Li
The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy
Complexity
title The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy
title_full The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy
title_fullStr The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy
title_full_unstemmed The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy
title_short The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy
title_sort study of a predator prey model with fear effect based on state dependent harvesting strategy
url http://dx.doi.org/10.1155/2022/9496599
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