O. V. Druzhinina, O. N. Masina
One of the important problem of nonlinear dynamical analysis and mathematical biology is the problem of stability of equilibria states and construction of phase portraits. The qualitative investigation of solutions in model of dynamics of populations described by the three ordinary nonlinear differential equations is carried out in the paper. The model is considered with regard to competition of species and diffusion rates and such that . Indicated model is the generalization of three-dimensional model of Zhang Xin-an and L. Chen on the case of differens diffusion rates. It was shown that considered model has four equilibria states. The conditions of existence of non-negative equilibria states are obtained. The stability in the Lyapunov sense of equilibria states is investigated. The local phase portraits are constructed.