Population Harvesting on both Prey and Predator

Aynalem Berhanie Emru; Purnachandra Rao Koya; Mohammed Yiha Dawed

doi:doi:10.11648/j.ajam.20170503.14

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Population Harvesting on both Prey and Predator

Aynalem Berhanie Emru, Purnachandra Rao Koya, Mohammed Yiha Dawed

Published in American Journal of Applied Mathematics (Volume 5, Issue 3)

Received: 29 April 2017 Accepted: 8 May 2017 Published: 29 June 2017

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Abstract

In this paper, the prey predator model as well as maximum sustainable yield has been discussed. Both prey and predator populations are considered to follow logistic law of growth. Both prey and predator harvesting or combined harvesting and maximum sustainable yield have been discussed. The maximum sustainable yield has been observed in two ways: as a function of one variable and also a function of two variables. Non-dimensionalization or scaling of the model, in order to reduce the number of the parameters has been performed. Positivity and boundedness of the solution have been studied. Stability analysis of the equilibrium point and also numerical simulations of the model in two dimensional as well as three dimensional cases have been done using MATLAB ode 45.

Published in	American Journal of Applied Mathematics (Volume 5, Issue 3)
DOI	10.11648/j.ajam.20170503.14
Page(s)	91-98
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), 2017. Published by Science Publishing Group

Keywords

Maximum Sustainable Yield, Stability, Combined Harvesting, Positivity and Boundedness, Simulation Study

References

[1]	Mohammed Yiha Dawed, Purnachandra Rao Koya and Temesgen Tibebu Mekonen, Generalist species predator-Prey model and maximum sustainable yield, IOSR Journal of Mathematics (IOSR-JM), Vol. 12, Issue 6, Ver. V, 2016, Pp 13-24. DOI: 10.9790/5728-1206051324
[2]	Susmita Paul, Paritosh Bhattacharya, K. S. Choudhury, Maximum Sustainable Yield Policy in Prey-Predator System-a study, 2013.
[3]	Kinfe Hailemariam Hntsa, Zenebe Taka Mengesha, Mathematical modeling of Fish Resources Harvesting with Predator at Maximum Sustainable Yield, 15 June 2016.
[4]	Jicai Huang and Yijun Gong, Bifurcation analysis in prey-predator model with constant-yield predator harvesting.
[5]	Mohamed Faris Laham, Ishtrinayagy S. Krishnarajah and Jamilah Mohd Shariff, Fish Harvesting Management Strategies Using Logistic Growth Model, 2012.
[6]	Corinne Wentworth, Optimum harvesting models for fishery population, summer of 2011.
[7]	T. K. Kar, and Bapan Ghosh, Impacts of maximum sustainable yield policy to prey-predator systems, 2013.
[8]	Predation, Wikipedia, the free encyclopedia.
[9]	K. Madhusudhan Reddy and K. Lakshmi Narayan A Prey-Predator Model with an Alternative Food for the Predator and Optimal Harvesting of the Prey, 2011.
[10]	Tapan Kumar Kar and Kunal Chakraborty effort dynamics in a prey-predator model with harvesting, International journal of informatics and system science 2010.
[11]	A brief explanation of biomass and maximum sustainable yield, Ministry of fisheries, July 2006.

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APA Style

Aynalem Berhanie Emru, Purnachandra Rao Koya, Mohammed Yiha Dawed. (2017). Population Harvesting on both Prey and Predator. American Journal of Applied Mathematics, 5(3), 91-98. https://doi.org/10.11648/j.ajam.20170503.14

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ACS Style

Aynalem Berhanie Emru; Purnachandra Rao Koya; Mohammed Yiha Dawed. Population Harvesting on both Prey and Predator. Am. J. Appl. Math. 2017, 5(3), 91-98. doi: 10.11648/j.ajam.20170503.14

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AMA Style

Aynalem Berhanie Emru, Purnachandra Rao Koya, Mohammed Yiha Dawed. Population Harvesting on both Prey and Predator. Am J Appl Math. 2017;5(3):91-98. doi: 10.11648/j.ajam.20170503.14

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@article{10.11648/j.ajam.20170503.14,
  author = {Aynalem Berhanie Emru and Purnachandra Rao Koya and Mohammed Yiha Dawed},
  title = {Population Harvesting on both Prey and Predator},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {3},
  pages = {91-98},
  doi = {10.11648/j.ajam.20170503.14},
  url = {https://doi.org/10.11648/j.ajam.20170503.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170503.14},
  abstract = {In this paper, the prey predator model as well as maximum sustainable yield has been discussed. Both prey and predator populations are considered to follow logistic law of growth. Both prey and predator harvesting or combined harvesting and maximum sustainable yield have been discussed. The maximum sustainable yield has been observed in two ways: as a function of one variable and also a function of two variables. Non-dimensionalization or scaling of the model, in order to reduce the number of the parameters has been performed. Positivity and boundedness of the solution have been studied. Stability analysis of the equilibrium point and also numerical simulations of the model in two dimensional as well as three dimensional cases have been done using MATLAB ode 45.},
 year = {2017}
}

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TY  - JOUR
T1  - Population Harvesting on both Prey and Predator
AU  - Aynalem Berhanie Emru
AU  - Purnachandra Rao Koya
AU  - Mohammed Yiha Dawed
Y1  - 2017/06/29
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170503.14
DO  - 10.11648/j.ajam.20170503.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 91
EP  - 98
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170503.14
AB  - In this paper, the prey predator model as well as maximum sustainable yield has been discussed. Both prey and predator populations are considered to follow logistic law of growth. Both prey and predator harvesting or combined harvesting and maximum sustainable yield have been discussed. The maximum sustainable yield has been observed in two ways: as a function of one variable and also a function of two variables. Non-dimensionalization or scaling of the model, in order to reduce the number of the parameters has been performed. Positivity and boundedness of the solution have been studied. Stability analysis of the equilibrium point and also numerical simulations of the model in two dimensional as well as three dimensional cases have been done using MATLAB ode 45.
VL  - 5
IS  - 3
ER  -

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Author Information

Aynalem Berhanie Emru

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
Purnachandra Rao Koya

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
Mohammed Yiha Dawed

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia

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APA Style

Aynalem Berhanie Emru, Purnachandra Rao Koya, Mohammed Yiha Dawed. (2017). Population Harvesting on both Prey and Predator. American Journal of Applied Mathematics, 5(3), 91-98. https://doi.org/10.11648/j.ajam.20170503.14

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ACS Style

Aynalem Berhanie Emru; Purnachandra Rao Koya; Mohammed Yiha Dawed. Population Harvesting on both Prey and Predator. Am. J. Appl. Math. 2017, 5(3), 91-98. doi: 10.11648/j.ajam.20170503.14

Copy | Download

AMA Style

Aynalem Berhanie Emru, Purnachandra Rao Koya, Mohammed Yiha Dawed. Population Harvesting on both Prey and Predator. Am J Appl Math. 2017;5(3):91-98. doi: 10.11648/j.ajam.20170503.14

Copy | Download

@article{10.11648/j.ajam.20170503.14,
  author = {Aynalem Berhanie Emru and Purnachandra Rao Koya and Mohammed Yiha Dawed},
  title = {Population Harvesting on both Prey and Predator},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {3},
  pages = {91-98},
  doi = {10.11648/j.ajam.20170503.14},
  url = {https://doi.org/10.11648/j.ajam.20170503.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170503.14},
  abstract = {In this paper, the prey predator model as well as maximum sustainable yield has been discussed. Both prey and predator populations are considered to follow logistic law of growth. Both prey and predator harvesting or combined harvesting and maximum sustainable yield have been discussed. The maximum sustainable yield has been observed in two ways: as a function of one variable and also a function of two variables. Non-dimensionalization or scaling of the model, in order to reduce the number of the parameters has been performed. Positivity and boundedness of the solution have been studied. Stability analysis of the equilibrium point and also numerical simulations of the model in two dimensional as well as three dimensional cases have been done using MATLAB ode 45.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Population Harvesting on both Prey and Predator
AU  - Aynalem Berhanie Emru
AU  - Purnachandra Rao Koya
AU  - Mohammed Yiha Dawed
Y1  - 2017/06/29
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170503.14
DO  - 10.11648/j.ajam.20170503.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 91
EP  - 98
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170503.14
AB  - In this paper, the prey predator model as well as maximum sustainable yield has been discussed. Both prey and predator populations are considered to follow logistic law of growth. Both prey and predator harvesting or combined harvesting and maximum sustainable yield have been discussed. The maximum sustainable yield has been observed in two ways: as a function of one variable and also a function of two variables. Non-dimensionalization or scaling of the model, in order to reduce the number of the parameters has been performed. Positivity and boundedness of the solution have been studied. Stability analysis of the equilibrium point and also numerical simulations of the model in two dimensional as well as three dimensional cases have been done using MATLAB ode 45.
VL  - 5
IS  - 3
ER  -

Copy | Download