Population Harvesting on both Prey and Predator
American Journal of Applied Mathematics
Volume 5, Issue 3, June 2017, Pages: 91-98
Received: Apr. 29, 2017;
Accepted: May 8, 2017;
Published: Jun. 29, 2017
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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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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.
Maximum Sustainable Yield, Stability, Combined Harvesting, Positivity and Boundedness, Simulation Study
To cite this article
Aynalem Berhanie Emru,
Purnachandra Rao Koya,
Mohammed Yiha Dawed,
Population Harvesting on both Prey and Predator, American Journal of Applied Mathematics.
Vol. 5, No. 3,
2017, pp. 91-98.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
Susmita Paul, Paritosh Bhattacharya, K. S. Choudhury, Maximum Sustainable Yield Policy in Prey-Predator System-a study, 2013.
Kinfe Hailemariam Hntsa, Zenebe Taka Mengesha, Mathematical modeling of Fish Resources Harvesting with Predator at Maximum Sustainable Yield, 15 June 2016.
Jicai Huang and Yijun Gong, Bifurcation analysis in prey-predator model with constant-yield predator harvesting.
Mohamed Faris Laham, Ishtrinayagy S. Krishnarajah and Jamilah Mohd Shariff, Fish Harvesting Management Strategies Using Logistic Growth Model, 2012.
Corinne Wentworth, Optimum harvesting models for fishery population, summer of 2011.
T. K. Kar, and Bapan Ghosh, Impacts of maximum sustainable yield policy to prey-predator systems, 2013.
Predation, Wikipedia, the free encyclopedia.
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.
Tapan Kumar Kar and Kunal Chakraborty effort dynamics in a prey-predator model with harvesting, International journal of informatics and system science 2010.
A brief explanation of biomass and maximum sustainable yield, Ministry of fisheries, July 2006.