Version 1
: Received: 15 March 2024 / Approved: 18 March 2024 / Online: 18 March 2024 (09:48:46 CET)
Version 2
: Received: 29 September 2024 / Approved: 14 October 2024 / Online: 14 October 2024 (11:26:55 CEST)
How to cite:
Makarov, D.; Parovik, R. Fractional Mathematical Models S.V. Dubovsky to Describe K-Waves in Economics. Preprints2024, 2024030995. https://doi.org/10.20944/preprints202403.0995.v1
Makarov, D.; Parovik, R. Fractional Mathematical Models S.V. Dubovsky to Describe K-Waves in Economics. Preprints 2024, 2024030995. https://doi.org/10.20944/preprints202403.0995.v1
Makarov, D.; Parovik, R. Fractional Mathematical Models S.V. Dubovsky to Describe K-Waves in Economics. Preprints2024, 2024030995. https://doi.org/10.20944/preprints202403.0995.v1
APA Style
Makarov, D., & Parovik, R. (2024). Fractional Mathematical Models S.V. Dubovsky to Describe K-Waves in Economics. Preprints. https://doi.org/10.20944/preprints202403.0995.v1
Chicago/Turabian Style
Makarov, D. and Roman Parovik. 2024 "Fractional Mathematical Models S.V. Dubovsky to Describe K-Waves in Economics" Preprints. https://doi.org/10.20944/preprints202403.0995.v1
Abstract
The article is devoted to the research of economic cycles and crises, which are studied within the framework of the theory of long waves by N. D. Kondratiev (K-waves) using the mathematical apparatus of fractional calculus. The object of the study is the mathematical model of S.V. Dubovsky 3 and some of its modifications, which describe the dynamics of the economic system, characterizing the interaction between the efficiency of new technologies and the efficiency of capital productivity. Modifications in the model are determined by the following points: the mathematical model takes into account the dependence of the rate of accumulation on capital productivity, there is an external harmonic influence - the influx of investments and new technological solutions, the economic system has heredity, including time-dependent, which leads to a delayed effect - the system’s response to impact. The property of heredity in the mathematical model is taken into account using fractional derivatives of constant and variable orders. Mathematical model S.V. Dubovsky and its modifications are studied numerically using the Adams-Bashforth-Moulton algorithm. Oscillograms and phase trajectories are constructed, and an interpretation of the simulation results is given.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
