O.V. Druzhinina1, V.L. Vorontsova2, D.S. Zaitsev3, M.A. Kabanov4, A.A. Shmelkova5 

1 Federal Research Center «Computer Science and Control» of Russian Academy of Sciences (Moscow, Russia)

2 Kazan Federal University (Verkhnyaya Pyshma, Russia)

3,4 Bunin Yelets State University (Yelets, Russia) 

The problems of synthesis and analysis of multidimensional nonlinear dynamic models of socio-economic processes are of both theoretical and applied interest. Due to the need to describe new qualitative effects, the solution of these problems is associated with the construction and study of systems of differential equations of various types, including systems of differential inclusions, fuzzy and stochastic differential equations. In particular, there is a need to switch to models with varying degrees of approximation given by systems similar to the Lorentz system and its generalizations. Shapovalov's model, called the average firm model, is used to describe microeconomic processes. The purpose of the article is to develop an approach to the study of multidimensional nonlinear dynamic models describing the processes of microeconomics, based on the application of methods of qualitative theory of differential equations and control theory. The design of multidimensional nonlinear dynamic models of socio-economic processes based on generalizations of the Shapovalov model is carried out. The case is considered when the development and interaction of several enterprises of the industry is modeled. Nonstationary models are considered when some of the model parameters depend on time. In addition, the construction of controlled models of enterprise development is proposed. The deterministic description of the models is supplemented by a description based on the apparatus of fuzzy and stochastic differential equations. An approach to the study of trajectory stability using the principle of reduction of the problem of stability of differential inclusions to the problems of stability of fuzzy and stochastic differential equations is considered. The results may be used in problems of synthesis, qualitative research and computer modeling of dynamic systems, as well as in optimization problems.

Druzhinina O.V., Vorontsova V.L., Zaitsev D. S., Kabanov M.A., Shmelkova A.A. Design and analysis of multidimensional  nonlinear dynamic models of socio-economic processes. Nonlinear World. 2021. V. 19. № 4. 2021. P. 5−14.  DOI: https://doi.org/10.18127/j20700970-202104-01 (In Russian)

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