Stability Analysis of Competition among Companies: A Guide from Predator Prey Modeling

Main Article Content

Titus Ifeanyi Chinebu
Nnaoma Ugenyi
Edmund Onwubiko Ezennorom

Abstract

This paper studied the behavior of two companies using predator prey model as the basis. As the companies are competing constantly, it affects them because their interaction determines the availability of resources for their growth. Considering growth of these companies, the parameters  which were respectively the carrying capacity and competitive impact of either of the competing companies on each other were included in the model. Equilibrium point and their existence criteria were analyzed to find the threshold that will guarantee the coexistence of both companies or collapse of either of them or both. It was shown that both companies can grow and rise simultaneously, (coexist) by dividing their resources correspondingly or that even the slightest change in their competition coefficient can lead to adverse situation, which may cause complete disappearance of one of the companies or both. We conclude that as long as these companies did not operate beyond their effective carrying capacity and equally maintain their respective competitive advantage, coexistence might be achieved. Some simulations are also given to illustrate our results.

Keywords:
Predator prey model, competition, competitive advantage, competitive coefficient, carrying capacity, resources.

Article Details

How to Cite
Chinebu, T. I., Ugenyi, N., & Ezennorom, E. O. (2020). Stability Analysis of Competition among Companies: A Guide from Predator Prey Modeling. Asian Research Journal of Mathematics, 16(1), 1-12. https://doi.org/10.9734/arjom/2020/v16i130166
Section
Original Research Article

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