The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator
In this paper, we study the chaotic regimes of the fractional Duffing oscillator. To do this, using the Wolf algorithm with Gram-Schmidt orthogonalization, we calculated the spectra of maximum Lyapunov exponents depending on the values of the control parameters, on the basis of which bifurcation dia...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2019-06-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20634/16881 |
| _version_ | 1828311307072307200 |
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| author | Roman Ivanovich Parovik |
| author_facet | Roman Ivanovich Parovik |
| author_sort | Roman Ivanovich Parovik |
| collection | DOAJ |
| description | In this paper, we study the chaotic regimes of the fractional Duffing oscillator. To do this, using the Wolf algorithm with Gram-Schmidt orthogonalization, we calculated the spectra of maximum Lyapunov exponents depending on the values of the control parameters, on the basis of which bifurcation diagrams were constructed. Bifurcation diagrams made it possible to determine areas in which a chaotic oscillatory regime exists. Phase trajectories were also constructed, which confirmed the research results. |
| first_indexed | 2024-04-13T15:56:47Z |
| format | Article |
| id | doaj.art-e71c828a263344bcaec93e5ec3080169 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-13T15:56:47Z |
| publishDate | 2019-06-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-e71c828a263344bcaec93e5ec30801692022-12-22T02:40:40ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812019-06-0123237839310.14498/vsgtu167818054The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillatorRoman Ivanovich Parovik0Institute of Cosmophysical Researches and Radio Wave Propagation, Far East Division, Russian Academy of SciencesIn this paper, we study the chaotic regimes of the fractional Duffing oscillator. To do this, using the Wolf algorithm with Gram-Schmidt orthogonalization, we calculated the spectra of maximum Lyapunov exponents depending on the values of the control parameters, on the basis of which bifurcation diagrams were constructed. Bifurcation diagrams made it possible to determine areas in which a chaotic oscillatory regime exists. Phase trajectories were also constructed, which confirmed the research results.https://journals.eco-vector.com/1991-8615/article/viewFile/20634/16881duffing-type fractal oscillatorgram-schmidt orthogonalizationwolf's algorithmmaximum exponent spectrumfractional derivative gerasimov-caputobifurcation diagramsphase trajectories |
| spellingShingle | Roman Ivanovich Parovik The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki duffing-type fractal oscillator gram-schmidt orthogonalization wolf's algorithm maximum exponent spectrum fractional derivative gerasimov-caputo bifurcation diagrams phase trajectories |
| title | The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator |
| title_full | The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator |
| title_fullStr | The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator |
| title_full_unstemmed | The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator |
| title_short | The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator |
| title_sort | existence of chaotic regimes of the fractional analogue of the duffing type oscillator |
| topic | duffing-type fractal oscillator gram-schmidt orthogonalization wolf's algorithm maximum exponent spectrum fractional derivative gerasimov-caputo bifurcation diagrams phase trajectories |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20634/16881 |
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