Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms
A non-linear fractional Selkov dynamic system for mathematical modeling of microseismic phenomena is proposed. This system is a generalization of the previously known Selkov system, which has self-oscillatory modes and is used in biology to describe glycolytic vibrations of the substrate and product...
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| Format: | Article |
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/22/4208 |
| _version_ | 1797464698160939008 |
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| author | Roman Ivanovich Parovik |
| author_facet | Roman Ivanovich Parovik |
| author_sort | Roman Ivanovich Parovik |
| collection | DOAJ |
| description | A non-linear fractional Selkov dynamic system for mathematical modeling of microseismic phenomena is proposed. This system is a generalization of the previously known Selkov system, which has self-oscillatory modes and is used in biology to describe glycolytic vibrations of the substrate and product. The Selkov fractional dynamical system takes into account the influence of heredity and is described using derivative fractional orders. The article investigates the Selkov fractional dynamic model using the Adams–Bashforth–Moulton numerical method, constructs oscillograms and phase trajectories, and studies the equilibrium points. Based on the spectra of the maximum Lyapunov exponents, it is shown that in the fractional dynamic model there can be relaxation and damped oscillations. |
| first_indexed | 2024-03-09T18:10:52Z |
| format | Article |
| id | doaj.art-6c2a274216c04a1fb9a449df65a75a01 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:10:52Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6c2a274216c04a1fb9a449df65a75a012023-11-24T09:07:45ZengMDPI AGMathematics2227-73902022-11-011022420810.3390/math10224208Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of MicroseismsRoman Ivanovich Parovik0Laboratory of Physical Process Modeling, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 7, Mirnaya St., Yelizovsky District, Paratunka 684034, RussiaA non-linear fractional Selkov dynamic system for mathematical modeling of microseismic phenomena is proposed. This system is a generalization of the previously known Selkov system, which has self-oscillatory modes and is used in biology to describe glycolytic vibrations of the substrate and product. The Selkov fractional dynamical system takes into account the influence of heredity and is described using derivative fractional orders. The article investigates the Selkov fractional dynamic model using the Adams–Bashforth–Moulton numerical method, constructs oscillograms and phase trajectories, and studies the equilibrium points. Based on the spectra of the maximum Lyapunov exponents, it is shown that in the fractional dynamic model there can be relaxation and damped oscillations.https://www.mdpi.com/2227-7390/10/22/4208fractional Selkov dynamic systemAdams–Bashforth–Moulton methodmicroseismsequilibrium pointsself-oscillationsphase trajectories |
| spellingShingle | Roman Ivanovich Parovik Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms Mathematics fractional Selkov dynamic system Adams–Bashforth–Moulton method microseisms equilibrium points self-oscillations phase trajectories |
| title | Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms |
| title_full | Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms |
| title_fullStr | Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms |
| title_full_unstemmed | Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms |
| title_short | Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms |
| title_sort | studies of the fractional selkov dynamical system for describing the self oscillatory regime of microseisms |
| topic | fractional Selkov dynamic system Adams–Bashforth–Moulton method microseisms equilibrium points self-oscillations phase trajectories |
| url | https://www.mdpi.com/2227-7390/10/22/4208 |
| work_keys_str_mv | AT romanivanovichparovik studiesofthefractionalselkovdynamicalsystemfordescribingtheselfoscillatoryregimeofmicroseisms |