Conditions of populations coexistence and stability analysis of dynamic models with migration flows

The research of population dynamics taking into account migration processes is a relevant scientific area. One of the key problems in this area is the analysis of mathematical models describing complex processes of interaction and migration of species in natural and artificial environments. Within the framework of the specified analysis of models, it is essential to obtain the coexistence conditions of species and the stability conditions of equilibrium states. The aim of the work is to describe dynamic models with migration flows, obtain the coexistence conditions of species, and analyze the stability of equilibrium states. For two classes of dynamic population models with migration flows, the issues of analytical and qualitative research are considered. The considered classes of models take into account competitive, trophic interactions and migration flows. Cases of uniform and uneven migration are studied. The coexistence conditions of species are obtained, the stability of positive equilibrium states is analyzed using Lyapunov functions. The results can find application in mathematical modeling problems of nonlinear dynamic systems, the description of which is used to analyze environmental, chemical, physical and sociological processes.