Dynamics of Predator-prey populations and The Influence of Allee effect

S.T. Motuma¹ , T.G. Beyene²

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.3 , pp.54-60, Jun-2020

Online published on Jun 30, 2020

Copyright © S.T. Motuma, T.G. Beyene . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, the interactions among three population species are studied. In these interactions, two mutuality prey population and a predator population are considered. Here, the first prey population considered as it is influenced by Allee effect while the second prey population is harvested and the predator population has alternative food source for survive. The three population interaction can be described as a food chain in which two preys help each other but the predator attacks both the preys following types of functional responses. These population interactions in ecology are modeled mathematically using ordinary differential equations.The biologically interesting equilibrium points of the system are identified and analyzed. The local and global stability analysis is carried out. Numerical examples of the model are conducted to support the results of the mathematical analysis. Finally, the results of the analysis and the discussion of the population dynamics areclearly studied.

Key-Words / Index Term :
predator, Assumptions, Normalization, Positivity, Allee effect, Functional response, Stability

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