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.
| Published in | Mathematical Modelling and Applications (Volume 5, Issue 2) |
| DOI | 10.11648/j.mma.20200502.12 |
| Page(s) | 55-64 |
| 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), 2020. Published by Science Publishing Group |
Prey – predator, Normalization, Positivity, Boundedness, Harvesting, Functional Response, Stability
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APA Style
Solomon Tolcha, Boka Kumsa Bole, Purnachandra Rao Koya. (2020). 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, 5(2), 55-64. https://doi.org/10.11648/j.mma.20200502.12
ACS Style
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. Math. Model. Appl. 2020, 5(2), 55-64. doi: 10.11648/j.mma.20200502.12
AMA Style
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. Math Model Appl. 2020;5(2):55-64. doi: 10.11648/j.mma.20200502.12
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Download@article{10.11648/j.mma.20200502.12,
author = {Solomon Tolcha and Boka Kumsa Bole and Purnachandra Rao Koya},
title = {Population Dynamics of Two Mutuality Preys and One Predator with Harvesting of One Prey and Allowing Alternative Food Source to Predator},
journal = {Mathematical Modelling and Applications},
volume = {5},
number = {2},
pages = {55-64},
doi = {10.11648/j.mma.20200502.12},
url = {https://doi.org/10.11648/j.mma.20200502.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200502.12},
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.},
year = {2020}
}
TY - JOUR T1 - Population Dynamics of Two Mutuality Preys and One Predator with Harvesting of One Prey and Allowing Alternative Food Source to Predator AU - Solomon Tolcha AU - Boka Kumsa Bole AU - Purnachandra Rao Koya Y1 - 2020/03/31 PY - 2020 N1 - https://doi.org/10.11648/j.mma.20200502.12 DO - 10.11648/j.mma.20200502.12 T2 - Mathematical Modelling and Applications JF - Mathematical Modelling and Applications JO - Mathematical Modelling and Applications SP - 55 EP - 64 PB - Science Publishing Group SN - 2575-1794 UR - https://doi.org/10.11648/j.mma.20200502.12 AB - 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. VL - 5 IS - 2 ER -
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