Economic dynamics models: theory, applications, computer aided implementation

In the paper, a survey of theoretical and applied results obtained in the framework of the scientific school at the Department of Information Systems and Mathematical Methods in Economics, Perm State University, is given. It covers the period from 2008 to 2015. The theoretical results are based on the principal statements of the contemporary theory of functional differential equations worked out by the participants of the Perm Seminar under the leadership of Prof. N.V. Azbelev (1922-2006). The focus of attention is on problems of forecasting, boundary value problems (problems of attainability), control problems, and problems of stability for the dynamic models that allow one to take into account aftereffects and effects of impulse disturbances (shocks). For the mentioned problems, sufficient conditions of the solvability are obtained, methods of constructing program controls and the corresponding trajectories are proposed. Algorithms of the computer-assisted study of the control problems are worked out, including algorithms of correction for certain ill-posed problems. The applied results use the achievements of the theory and are implemented in the form of software tools for the study and solution of the real economy problems such as forecasting, control and stability analysis as applied to models of socio-economic development of the regions of the Russian Federation and the Russian Economy as a whole.