This work touches upon the tasks of describing regional socio-economic development. The nature of the considered problem indicates the fact that the only relevant tool here is mathematical modeling. In this paper, the application of mathematical modeling is considered for the problem of managing regional development. The results of calculations based on the regional dynamic model that passes through the hierarchy of instabilities (the correspondence of the same stationary points of the model to different parameters) are presented. These instabilities lead to increasingly complex structures.