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

Rui-Ling Zhang; Wan-Xiong Wang; Li-Juan Qin

doi:doi:10.11648/j.acm.20150401.14

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

Rui-Ling Zhang, Wan-Xiong Wang, Li-Juan Qin

Published in Applied and Computational Mathematics (Volume 4, Issue 1)

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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APA Style

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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TY  - JOUR
T1  - Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation
AU  - Rui-Ling Zhang
AU  - Wan-Xiong Wang
AU  - Li-Juan Qin
Y1  - 2015/02/02
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150401.14
DO  - 10.11648/j.acm.20150401.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 20
EP  - 29
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150401.14
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

Rui-Ling Zhang

College of Resources and Environmental Science, Gansu Agricultural University, Gansu 730070, PR China
Wan-Xiong Wang

College of Resources and Environmental Science, Gansu Agricultural University, Gansu 730070, PR China
Li-Juan Qin

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

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Plain Text BibTeX RIS

APA Style

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Optimal Harvesting Policy of Discrete-Time Predator-Prey Dynamic System with Holling Type-IV Functional Response and Its Simulation
AU  - Rui-Ling Zhang
AU  - Wan-Xiong Wang
AU  - Li-Juan Qin
Y1  - 2015/02/02
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150401.14
DO  - 10.11648/j.acm.20150401.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 20
EP  - 29
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150401.14
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  -

Copy | Download