Selkov’s Dynamic System of Fractional Variable Order with Non-Constant Coefficients
This article uses an approach based on the triad model–algorithm–program. The model is a nonlinear dynamic Selkov system with non-constant coefficients and fractional derivatives of the Gerasimov–Caputo type. The Adams–Bashforth–Multon numerical method from the predictor–corrector family of methods...
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MDPI AG
2025-01-01
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| author | Roman Parovik |
| author_facet | Roman Parovik |
| author_sort | Roman Parovik |
| collection | DOAJ |
| description | This article uses an approach based on the triad model–algorithm–program. The model is a nonlinear dynamic Selkov system with non-constant coefficients and fractional derivatives of the Gerasimov–Caputo type. The Adams–Bashforth–Multon numerical method from the predictor–corrector family of methods is selected as an algorithm for studying this system. The ABMSelkovFracSim 1.0 software package acts as a program, in which a numerical algorithm with the ability to visualize the research results is implemented to build oscillograms and phase trajectories. Examples of the ABMSelkovFracSim 1.0 software package operation for various values of the model parameters are given. It is shown that with an increase in the values of the parameter responsible for the characteristic time scale, regular and chaotic modes are observed. Further in this work, bifurcation diagrams are constructed, which confirm this. Aperiodic modes are also detected and a singularity is revealed. |
| format | Article |
| id | doaj-art-bf6efbe467104fbd907239087d3ab6d4 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-bf6efbe467104fbd907239087d3ab6d42025-08-20T02:48:09ZengMDPI AGMathematics2227-73902025-01-0113337210.3390/math13030372Selkov’s Dynamic System of Fractional Variable Order with Non-Constant CoefficientsRoman Parovik0Laboratory of Physical Process Modeling, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 684034 Paratunka, RussiaThis article uses an approach based on the triad model–algorithm–program. The model is a nonlinear dynamic Selkov system with non-constant coefficients and fractional derivatives of the Gerasimov–Caputo type. The Adams–Bashforth–Multon numerical method from the predictor–corrector family of methods is selected as an algorithm for studying this system. The ABMSelkovFracSim 1.0 software package acts as a program, in which a numerical algorithm with the ability to visualize the research results is implemented to build oscillograms and phase trajectories. Examples of the ABMSelkovFracSim 1.0 software package operation for various values of the model parameters are given. It is shown that with an increase in the values of the parameter responsible for the characteristic time scale, regular and chaotic modes are observed. Further in this work, bifurcation diagrams are constructed, which confirm this. Aperiodic modes are also detected and a singularity is revealed.https://www.mdpi.com/2227-7390/13/3/372fractional Selkov dynamic systemfractional derivative of variable orderAdams–Bashforth–Moulton methodsoftware package ABMSelkovFracSim 1.0phase trajectoriesoscillograms |
| spellingShingle | Roman Parovik Selkov’s Dynamic System of Fractional Variable Order with Non-Constant Coefficients Mathematics fractional Selkov dynamic system fractional derivative of variable order Adams–Bashforth–Moulton method software package ABMSelkovFracSim 1.0 phase trajectories oscillograms |
| title | Selkov’s Dynamic System of Fractional Variable Order with Non-Constant Coefficients |
| title_full | Selkov’s Dynamic System of Fractional Variable Order with Non-Constant Coefficients |
| title_fullStr | Selkov’s Dynamic System of Fractional Variable Order with Non-Constant Coefficients |
| title_full_unstemmed | Selkov’s Dynamic System of Fractional Variable Order with Non-Constant Coefficients |
| title_short | Selkov’s Dynamic System of Fractional Variable Order with Non-Constant Coefficients |
| title_sort | selkov s dynamic system of fractional variable order with non constant coefficients |
| topic | fractional Selkov dynamic system fractional derivative of variable order Adams–Bashforth–Moulton method software package ABMSelkovFracSim 1.0 phase trajectories oscillograms |
| url | https://www.mdpi.com/2227-7390/13/3/372 |
| work_keys_str_mv | AT romanparovik selkovsdynamicsystemoffractionalvariableorderwithnonconstantcoefficients |