Population Dynamics of Two Mutuality Preys and One Predator with Harvesting of One Prey and Allowing Alternative Food Source to Predator
Mathematical Modelling and Applications
Volume 5, Issue 2, June 2020, Pages: 55-64
Received: Jan. 1, 2020; Accepted: Mar. 13, 2020; Published: Mar. 31, 2020
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Authors
Solomon Tolcha, Department of Mathematics, Addis Ababa Science and Technology University, Addis Ababa, Ethiopia
Boka Kumsa Bole, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Wollega University, Nekemte, Ethiopia
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Abstract
In this paper, the interactions among three species populations are considered. The system includes two mutuality preys and one predator. The second prey is harvested. While dependent on preys, the predator has an alternative food source also. The three species interaction can be described as a food chain in which two preys help each other but the predator attacks both the preys according to type I and II functional responses respectively. These population interactions are modeled mathematically using ordinary differential equations. It is shown that the solution of the model is both positive and bounded. The equilibrium points of the model are found and they are analyzed to identify a threshold that will guarantee the coexistence of the populations. Positive equilibrium points of the system are identified and their local and global stability analysis is carried out. Numerical simulation study of the model is conducted to support the results of the mathematical analysis. It is pointed out that as long as harvesting rate on the prey population is smaller than its intrinsic growth rate the coexistence of the system can be achieve. The results of the analysis and the discussion of the population dynamics is lucidly presented in the text of the paper.
Keywords
Prey – predator, Normalization, Positivity, Boundedness, Harvesting, Functional Response, Stability
To cite this article
Solomon Tolcha, Boka Kumsa Bole, Purnachandra Rao Koya, Population Dynamics of Two Mutuality Preys and One Predator with Harvesting of One Prey and Allowing Alternative Food Source to Predator, Mathematical Modelling and Applications. Vol. 5, No. 2, 2020, pp. 55-64. doi: 10.11648/j.mma.20200502.12
Copyright
Copyright © 2020 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.
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