Modeling the dynamics of two-factor socio-economic states through mappings close to extension
https://doi.org/10.26425/1816-4277-2022-8-104-110
Abstract
A new way of developing a mathematical model of the dynamics of the factors forming the considered social, political, economic, ecological or other space of life activity of society, depending on local changes in parameters affecting these factors, is presented. A feature of the proposed approach is the use of a matrix of marginal values included in the study that make up the Jacobi matrix of noted factors. The dependence of the factors describing the socio-economic system on the parameters of the model is obtained in explicit form. Under certain conditions, the described relations have the form of mappings close to extension. A generalized assessment of these transformations is proposed. Accounting for this assessment is important for preventing crisis phenomena. The model is intended to be used for informational, forecasting, management and governance purposes in the presence of a sufficient digitalization’s degree of public structures, without which it is problematic to receive and transmit data for building the model, and perform related calculations.
About the Author
V. V. EgorovRussian Federation
Cand. Sci. (Phys. and Math.), Assoc. Prof. at the Mathematical Methods in Economics and Management Department,
Moscow
References
1. Kahneman D., Tversky A. Prospect Theory: An Analysis of Decision Under Risk. In: MacLean L. and Ziemba W. (eds.) Handbook of the Fundamentals of Financial Decision Making. World Scientific Publishing Company; 2013. P. 99–127. https://doi.org/10.1142/9789814417358_0006
2. Reshetnyak Yu.G. Stability theorems in geometry and analysis: monograph. Novosibirsk: Sobolev Institute of Mathematics Publ. House; 1996. (In Russian).
3. Ahlfors L.V. Möbius transformations in several dimensions. Minneapolis: University of Minnesota; 1981.
4. Bellman R. Dynamic programming. Dover Publications Inc.; 2003.
5. Reshetnyak Yu.G. Space mappings with bounded distortion. Providence: American Mathematical Society; 1989.
6. Egorov V.V. On a system of differential equations describing mappings with bounded distortion. Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1: Matematika, fizika. 2004;(8):18–27.
7. Corriou J.-P. Numerical Methods and Optimization: Theory and Practice for Engineers. Springer; 2021.
8. Ros F, Guillaume S. Sampling Techniques for Supervised or Unsupervised Tasks. Springer; 2020.
9. Borovkov A.A. Probability Theory. Springer; 2013.
10. Cobzaş S., Miculescu R., Nicolae A. Lipschitz Functions. Springer; 2019.
11. Egorov V.V. Recovering of a mapping via Jacobi matrix normalized by a homogeneous function. Izvestiya of Saratov University. Series: Mathematics. Mechanics. Informatics. 2007;7(2):14–20. https://doi.org/10.18500/1816-9791-2007-7-2-14-20
12. D’Acci L. (ed.) The Mathematics of Urban Morphology. Springer, Birkhäuser; 2019.
13. Munda G. Social Multi-Criteria Evaluation For a Sustainable Economy. Springer; 2008.
14. Diligenskii N.V., Dymova L.G., Sevastianov P.V. Fuzzy modeling and multicriteria optimization of production systems under uncertainty: technology, economics, ecology. Moscow: Mashinostroenie-1; 2004. (In Russian).
Review
For citations:
Egorov V.V. Modeling the dynamics of two-factor socio-economic states through mappings close to extension. Vestnik Universiteta. 2022;(8):104-110. (In Russ.) https://doi.org/10.26425/1816-4277-2022-8-104-110