Mathematical Model of Population Interactions with Functional Responses and Harvesting Function

S. T. Motuma¹

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.3 , pp.33-38, Jun-2020

Online published on Jun 30, 2020

Copyright © S. T. Motuma . 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, ecological interaction between two population species has been studied. Mutuality interaction has been considered between two populations. Without interactions both population grow logistically. The interaction between populations are proceeding following different types of functional responses and harvesting function. In these interactions, the population species are harvested proportionally. The proportional harvesting is introduced to the interaction in order to describe the removal of population from their habitat based on their density. According to this, both populations are harvested in this model. In order to study these interactions mathematical equation is constructed. It is shown that the model equation have both positive and bounded solutions. The dynamics of these populations have been studied. Local and global stability analysis is carried out based on the positive equilibrium point. Numerical simulations supporting theoretical results are also included here.

Key-Words / Index Term :
Mutualism, Lyapunov function, Phase plane, Functional Response, Positivity, Boundedness and proportional Harvesting.

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