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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
Volume 5, Issue 3, September 2020, Pages: 156-166
Received: May 1, 2020; Accepted: Jun. 18, 2020; Published: Aug. 4, 2020
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Authors
Geremew Kenassa Edessa, 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, 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.
Keywords
Prey, Predator, Ammensal, Commensal, Host, Continuous Time, Stability, Numerical Simulation
To cite this article
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, Mathematical Modelling and Applications. Vol. 5, No. 3, 2020, pp. 156-166. doi: 10.11648/j.mma.20200503.14
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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