On modification and application of Lotka-Volterra competition model

Lotka-Volterra competition model has been applied in many areas, including in biological systems and market-share competition in economics. In this paper, we study a modified version of the two-species competition model where the growth of the first population follows the exponential growth model. The modified model has three equilibria namely the extinction equilibrium, the coexistence equilibrium, and the extinction of first population equilibrium. We found that the extinction equilibrium and the coexistence equilibrium are unstable. We also found that the extinction of the first population is conditionally asymptotically stable. Furthermore, we estimated parameters of the modified model from competition data of two Paramecium species, where the data cited from literature.