In this paper, a three species eco system, involving three pairs is considered modeled to examine the stability. Among the three species, one plays dual roles which are a host and an enemy with Monod response. In the first place model assumptions and formulation was carried out for investigations. The biological feasibility of the system is checked. That is positivity and boundedness of the model is verified. It is shown that biologically valid. The dynamical behavior of the proposed model system was analyzed qualitatively. The dynamical analysis includes the determination of all possible equilibrium points and their stability properties. All the equilibrium states are identified and the local asymptotic stability of some of the equilibrium states is examined by considering the set criteria. It is observed that among the states, the state in which the Prey and its Host species are exist is stable and the state where the Predator/Ammensal species is washed out is asymptotically stable. The global stability of the co-existence of the species was investigated by constructing a suitable Lyapunov function. To support our analytical studies, some numerical simulations was performed susing some mathematical software and the results were forwarded in the last section.
| Published in | Mathematical Modelling and Applications (Volume 5, Issue 3) |
| DOI | 10.11648/j.mma.20200503.14 |
| Page(s) | 156-166 |
| 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, Ammensal, Commensal, Host, Continuous Time, Stability, Numerical Simulation
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APA Style
Geremew Kenassa Edessa, Purnachandra Rao Koya. (2020). Modeling and Stability Analysis of a Three Species Ecosystem with the Third Species Response to the First Species in Sigmoid Functional Response Form. Mathematical Modelling and Applications, 5(3), 156-166. https://doi.org/10.11648/j.mma.20200503.14
ACS Style
Geremew Kenassa Edessa; Purnachandra Rao Koya. Modeling and Stability Analysis of a Three Species Ecosystem with the Third Species Response to the First Species in Sigmoid Functional Response Form. Math. Model. Appl. 2020, 5(3), 156-166. doi: 10.11648/j.mma.20200503.14
AMA Style
Geremew Kenassa Edessa, Purnachandra Rao Koya. Modeling and Stability Analysis of a Three Species Ecosystem with the Third Species Response to the First Species in Sigmoid Functional Response Form. Math Model Appl. 2020;5(3):156-166. doi: 10.11648/j.mma.20200503.14
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Download@article{10.11648/j.mma.20200503.14,
author = {Geremew Kenassa Edessa and Purnachandra Rao Koya},
title = {Modeling and Stability Analysis of a Three Species Ecosystem with the Third Species Response to the First Species in Sigmoid Functional Response Form},
journal = {Mathematical Modelling and Applications},
volume = {5},
number = {3},
pages = {156-166},
doi = {10.11648/j.mma.20200503.14},
url = {https://doi.org/10.11648/j.mma.20200503.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200503.14},
abstract = {In this paper, a three species eco system, involving three pairs is considered modeled to examine the stability. Among the three species, one plays dual roles which are a host and an enemy with Monod response. In the first place model assumptions and formulation was carried out for investigations. The biological feasibility of the system is checked. That is positivity and boundedness of the model is verified. It is shown that biologically valid. The dynamical behavior of the proposed model system was analyzed qualitatively. The dynamical analysis includes the determination of all possible equilibrium points and their stability properties. All the equilibrium states are identified and the local asymptotic stability of some of the equilibrium states is examined by considering the set criteria. It is observed that among the states, the state in which the Prey and its Host species are exist is stable and the state where the Predator/Ammensal species is washed out is asymptotically stable. The global stability of the co-existence of the species was investigated by constructing a suitable Lyapunov function. To support our analytical studies, some numerical simulations was performed susing some mathematical software and the results were forwarded in the last section.},
year = {2020}
}
TY - JOUR T1 - Modeling and Stability Analysis of a Three Species Ecosystem with the Third Species Response to the First Species in Sigmoid Functional Response Form AU - Geremew Kenassa Edessa AU - Purnachandra Rao Koya Y1 - 2020/08/04 PY - 2020 N1 - https://doi.org/10.11648/j.mma.20200503.14 DO - 10.11648/j.mma.20200503.14 T2 - Mathematical Modelling and Applications JF - Mathematical Modelling and Applications JO - Mathematical Modelling and Applications SP - 156 EP - 166 PB - Science Publishing Group SN - 2575-1794 UR - https://doi.org/10.11648/j.mma.20200503.14 AB - In this paper, a three species eco system, involving three pairs is considered modeled to examine the stability. Among the three species, one plays dual roles which are a host and an enemy with Monod response. In the first place model assumptions and formulation was carried out for investigations. The biological feasibility of the system is checked. That is positivity and boundedness of the model is verified. It is shown that biologically valid. The dynamical behavior of the proposed model system was analyzed qualitatively. The dynamical analysis includes the determination of all possible equilibrium points and their stability properties. All the equilibrium states are identified and the local asymptotic stability of some of the equilibrium states is examined by considering the set criteria. It is observed that among the states, the state in which the Prey and its Host species are exist is stable and the state where the Predator/Ammensal species is washed out is asymptotically stable. The global stability of the co-existence of the species was investigated by constructing a suitable Lyapunov function. To support our analytical studies, some numerical simulations was performed susing some mathematical software and the results were forwarded in the last section. VL - 5 IS - 3 ER -
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