Dubovsky’s Class of Mathematical Models for Describing Economic Cycles with Heredity Effects
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| Udgivet i: | Fractal and Fractional vol. 9, no. 1 (2025), p. 19 |
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| Andre forfattere: | , |
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| Online adgang: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 022 | |a 2504-3110 | ||
| 024 | 7 | |a 10.3390/fractalfract9010019 |2 doi | |
| 035 | |a 3159507321 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 100 | 1 | |a Makarov, Danil |u Department of Applied Mathematics and Computer Analysis, National University of Uzbekistan Named After Mirzo Ulugbek, Tashkent 100174, Uzbekistan; <email>danil.makarov.pk@yandex.ru</email> (D.M.); | |
| 245 | 1 | |a Dubovsky’s Class of Mathematical Models for Describing Economic Cycles with Heredity Effects | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a The article is devoted to the study of economic cycles and crises, which are studied within the framework of the theory of N.D. Kondratiev long waves (K-waves). The object of the study is the fractional mathematical models of S. V. Dubovsky, consisting of two nonlinear differential equations of fractional order and describing the dynamics of the efficiency of new technologies and the efficiency of capital productivity, taking into account constant and variable heredity. Fractional mathematical models also take into account the dependence of the rate of accumulation on capital productivity and the influx of external investment and new technological solutions. The effects of heredity lead to a delayed effect of the response of the system in question to the impact. The property of heredity in mathematical models is taken into account using fractional derivatives of constant and variable orders in the sense of Gerasimov–Caputo. The fractional mathematical models of S. V. Dubovsky are further studied numerically using the Adams–Bashforth–Moulton algorithm. Using a numerical algorithm, oscillograms and phase trajectories were constructed for various values and model parameters. It is shown that the fractional mathematical models of S. V. Dubovsky may have limit cycles, which are not always stable. | |
| 653 | |a Calculus | ||
| 653 | |a Heredity | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Mathematical models | ||
| 653 | |a Nonlinear differential equations | ||
| 653 | |a Capital depreciation | ||
| 653 | |a Cauchy problems | ||
| 653 | |a Numerical analysis | ||
| 653 | |a Productivity | ||
| 653 | |a Business cycles | ||
| 653 | |a Variables | ||
| 653 | |a Algorithms | ||
| 653 | |a Gross Domestic Product--GDP | ||
| 653 | |a Economic theory | ||
| 653 | |a Nonlinear dynamics | ||
| 653 | |a Production functions | ||
| 653 | |a Ordinary differential equations | ||
| 653 | |a Technology | ||
| 653 | |a Efficiency | ||
| 700 | 1 | |a Parovik, Roman |u Department of Applied Mathematics and Computer Analysis, National University of Uzbekistan Named After Mirzo Ulugbek, Tashkent 100174, Uzbekistan; <email>danil.makarov.pk@yandex.ru</email> (D.M.); ; Laboratory of Physical Process Modeling, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 684034 Paratunka, Russia | |
| 700 | 1 | |a Rakhmonov, Zafar |u Department of Applied Mathematics and Computer Analysis, National University of Uzbekistan Named After Mirzo Ulugbek, Tashkent 100174, Uzbekistan; <email>danil.makarov.pk@yandex.ru</email> (D.M.); | |
| 773 | 0 | |t Fractal and Fractional |g vol. 9, no. 1 (2025), p. 19 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3159507321/abstract/embedded/H09TXR3UUZB2ISDL?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3159507321/fulltextwithgraphics/embedded/H09TXR3UUZB2ISDL?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3159507321/fulltextPDF/embedded/H09TXR3UUZB2ISDL?source=fedsrch |