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.
| Published in | American Journal of Applied Mathematics (Volume 6, Issue 3) |
| DOI | 10.11648/j.ajam.20180603.12 |
| Page(s) | 109-116 |
| 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), 2018. Published by Science Publishing Group |
Mutualism, Functional Response, Harvesting, Phase Plane Analysis, Positivity and Boundedness
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APA Style
Solomon Tolcha, Boka Kumsa, Purnachandra Rao Koya. (2018). Modeling and Simulation Study of Mutuality Interactions with Type II functional Response and Harvesting. American Journal of Applied Mathematics, 6(3), 109-116. https://doi.org/10.11648/j.ajam.20180603.12
ACS Style
Solomon Tolcha; Boka Kumsa; Purnachandra Rao Koya. Modeling and Simulation Study of Mutuality Interactions with Type II functional Response and Harvesting. Am. J. Appl. Math. 2018, 6(3), 109-116. doi: 10.11648/j.ajam.20180603.12
AMA Style
Solomon Tolcha, Boka Kumsa, Purnachandra Rao Koya. Modeling and Simulation Study of Mutuality Interactions with Type II functional Response and Harvesting. Am J Appl Math. 2018;6(3):109-116. doi: 10.11648/j.ajam.20180603.12
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Download@article{10.11648/j.ajam.20180603.12,
author = {Solomon Tolcha and Boka Kumsa and Purnachandra Rao Koya},
title = {Modeling and Simulation Study of Mutuality Interactions with Type II functional Response and Harvesting},
journal = {American Journal of Applied Mathematics},
volume = {6},
number = {3},
pages = {109-116},
doi = {10.11648/j.ajam.20180603.12},
url = {https://doi.org/10.11648/j.ajam.20180603.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20180603.12},
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.},
year = {2018}
}
TY - JOUR T1 - Modeling and Simulation Study of Mutuality Interactions with Type II functional Response and Harvesting AU - Solomon Tolcha AU - Boka Kumsa AU - Purnachandra Rao Koya Y1 - 2018/07/31 PY - 2018 N1 - https://doi.org/10.11648/j.ajam.20180603.12 DO - 10.11648/j.ajam.20180603.12 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 109 EP - 116 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20180603.12 AB - 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. VL - 6 IS - 3 ER -
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