Analysis of The Competition Model of Two Populations Around The Orbit of The Equilibrium Point

Abstract

The competition of two populations model that represented in an ordinary differential equations system. This model describes about the competition of two population in general that is consist of the interspesies competition and the intraspesies competition. In ecology, the population dynamic is closely related to population growth, equilibrium, and stability. Equilibrium is represented by a point called the equilibrium point or fixed point. By analyzing the stability around the fixed point, it can be seen the carrying capacity of a system, which mean the optimal number of individual that can be supported by the environment. According to the analysis of the model obtained 4 fixed points, three of them are unstable and the other else is stable. The orbit of the system around fixed point visualized using software. The behavior orbit around fixed point of the model will move away from the unstable fixed point and move closer to the stable fixed point.