In this talk we will consider a community of two mutually competing species modeled by the Lotka–Volterra type system:formulawhere xi(t) is the population size of the i-th species at time t, x_ i denote dxi dt and all coefficients aij , bi are strictly positive real numbers. This kind of ordinary differential equations systems represent a class of Kolmogorov systems and they are widely used in the mathematical models for the dynamics of population, like predator-prey models or different models for the spread of diseases. A qualitative analysis of this two dimensional Lotka–Volterra system based on dynamical systems theory will be performed, by studying the local behavior of the equilibria and obtaining local dynamics properties both from the linear (Lyapunov) stability and Jacobi stability point of view.