Modeling and Simulation Study of Mutuality Interactions with Type II functional Response and Harvesting
American Journal of Applied Mathematics
Volume 6, Issue 3, June 2018, Pages: 109-116
Received: May 25, 2018; Accepted: Jun. 26, 2018; Published: Jul. 31, 2018
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Authors
Solomon Tolcha, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Boka Kumsa, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Hawassa University, Hawassa, Ethiopia
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Abstract
This paper deals with the study of mutuality interactions between two species population with type II functional response and also with the inclusion of harvesting. Harvesting functions are introduced to express the rate of reductions of the species separately. Mathematical model have been constructed and considered for the analysis and results. In this model, the first population species benefited according to type II functional response and the second species benefited from the first according to type I functional response and also harvested proportional to its density. It is shown that the model has positive and bounded solutions. Stability analysis is carried out. The local and global stability of biologically interested equilibrium point are considered and analyzed. Numerical examples supporting theoretical results such as phase plane and simulation study using DSolver are also included. Assumptions and results are presented and discussed lucidly in the text of the paper.
Keywords
Mutualism, Functional Response, Harvesting, Phase Plane Analysis, Positivity and Boundedness
To cite this article
Solomon Tolcha, Boka Kumsa, Purnachandra Rao Koya, Modeling and Simulation Study of Mutuality Interactions with Type II functional Response and Harvesting, American Journal of Applied Mathematics. Vol. 6, No. 3, 2018, pp. 109-116. doi: 10.11648/j.ajam.20180603.12
Copyright
Copyright © 2018 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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