Applied mathematics which means the use of mathematics in solving natural phenomena, both physical phenomena and non-physical phenomena. Applied mathematics in ecology is mathematical models. Mathematical models can represent a population of living things are the Mathematical Model of two-population competition, the mathematical model of two-population competition is Interactions that occur between individuals in one species or interactions between individuals with different species and have a negative impact on both are called competition. based on the results of the analysis obtained 4 equilibrium points, while the stability of the equilibrium point of the system also fulfills 4 conditions.
Keywords: applied mathematics, model of the two-population competition, equilibrium, stability of the equilibrium.