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Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation

Received: 14 November 2014     Accepted: 29 November 2014     Published: 2 February 2015
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Abstract

This paper deals with a discrete-time prey-predator system with Holling type-IV function response in the presence of some alternative food to predator and harvesting of prey species. By theoretical analysis and numerical simulation, comparing with the system without harvesting, ecological equilibrium point of the system is removed if harvesting effort is changed, and the appropriate harvesting effort can increase the stability of the system. Moreover, optimal harvesting policy is obtained using Pontryagin’s maximum principle. Meanwhile, some numerical simulations verify our analytical results. This study also gains the maximum economic profit which is based on the ecological equilibrium. The suitable price of resources can control the excessive harvest to promote the sustainable development of species.

Published in Applied and Computational Mathematics (Volume 4, Issue 1)
DOI 10.11648/j.acm.20150401.14
Page(s) 20-29
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Discrete-Time Predator-Prey Model, Equilibrium, Pontryagin Maximum Principle, Bifurcation, Sustainable Development

References
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    Rui-Ling Zhang, Wan-Xiong Wang, Li-Juan Qin. (2015). Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation. Applied and Computational Mathematics, 4(1), 20-29. https://doi.org/10.11648/j.acm.20150401.14

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    ACS Style

    Rui-Ling Zhang; Wan-Xiong Wang; Li-Juan Qin. Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation. Appl. Comput. Math. 2015, 4(1), 20-29. doi: 10.11648/j.acm.20150401.14

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    AMA Style

    Rui-Ling Zhang, Wan-Xiong Wang, Li-Juan Qin. Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation. Appl Comput Math. 2015;4(1):20-29. doi: 10.11648/j.acm.20150401.14

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  • @article{10.11648/j.acm.20150401.14,
      author = {Rui-Ling Zhang and Wan-Xiong Wang and Li-Juan Qin},
      title = {Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation},
      journal = {Applied and Computational Mathematics},
      volume = {4},
      number = {1},
      pages = {20-29},
      doi = {10.11648/j.acm.20150401.14},
      url = {https://doi.org/10.11648/j.acm.20150401.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150401.14},
      abstract = {This paper deals with a discrete-time prey-predator system with Holling type-IV function response in the presence of some alternative food to predator and harvesting of prey species. By theoretical analysis and numerical simulation, comparing with the system without harvesting, ecological equilibrium point of the system is removed if harvesting effort is changed, and the appropriate harvesting effort can increase the stability of the system. Moreover, optimal harvesting policy is obtained using Pontryagin’s maximum principle. Meanwhile, some numerical simulations verify our analytical results. This study also gains the maximum economic profit which is based on the ecological equilibrium. The suitable price of resources can control the excessive harvest to promote the sustainable development of species.},
     year = {2015}
    }
    

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    AU  - Rui-Ling Zhang
    AU  - Wan-Xiong Wang
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    AB  - This paper deals with a discrete-time prey-predator system with Holling type-IV function response in the presence of some alternative food to predator and harvesting of prey species. By theoretical analysis and numerical simulation, comparing with the system without harvesting, ecological equilibrium point of the system is removed if harvesting effort is changed, and the appropriate harvesting effort can increase the stability of the system. Moreover, optimal harvesting policy is obtained using Pontryagin’s maximum principle. Meanwhile, some numerical simulations verify our analytical results. This study also gains the maximum economic profit which is based on the ecological equilibrium. The suitable price of resources can control the excessive harvest to promote the sustainable development of species.
    VL  - 4
    IS  - 1
    ER  - 

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Author Information
  • College of Resources and Environmental Science, Gansu Agricultural University, Gansu 730070, PR China

  • College of Resources and Environmental Science, Gansu Agricultural University, Gansu 730070, PR China

  • College of Resources and Environmental Science, Gansu Agricultural University, Gansu 730070, PR China

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