Analysis of a fractional-order chaotic system in the context of the Caputo fractional derivative via bifurcation and Lyapunov exponents
This research focuses on the characterization of the chaotic behaviors, the hyperchaotic behaviors, and the impact of the fractional-order derivative in a class of fractional chaotic system. The numerical scheme, including the discretization of the Riemann–Liouville derivative, will be used to depic...
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| Format: | Article |
| Language: | English |
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Elsevier
2021-01-01
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| Series: | Journal of King Saud University: Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018364720303888 |
| _version_ | 1818447843341369344 |
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| author | Ndolane Sene |
| author_facet | Ndolane Sene |
| author_sort | Ndolane Sene |
| collection | DOAJ |
| description | This research focuses on the characterization of the chaotic behaviors, the hyperchaotic behaviors, and the impact of the fractional-order derivative in a class of fractional chaotic system. The numerical scheme, including the discretization of the Riemann–Liouville derivative, will be used to depict the phase portraits of the fractional-order chaotic system when the order of the used fractional-order derivative takes different values. The impact of the fractional-order derivative in the fractional chaotic system will be investigated. The proposed numerical scheme proposes a new alternative to obtain the phase portraits of the fractional-order chaotic systems. The sensitivity of the chaotic systems to the changes in the initial condition and the variation of the parameters of the considered model will be focussed with precision using the bifurcation diagrams and the Lyapunov exponent. The stability of the equilibrium points of the commensurable fractional-order chaotic system will be addressed in the context of fractional calculus. In other words, we will use the standard Matignon criterion to address the problem of stability. The main attraction and novelty of this paper will be the use of the Lyapunov exponent to characterize the nature of chaos and to prove the dissipativity of the considered chaotic system. |
| first_indexed | 2024-12-14T20:10:03Z |
| format | Article |
| id | doaj.art-d33bc245fa1e4d08b5fc688dfd24ab7e |
| institution | Directory Open Access Journal |
| issn | 1018-3647 |
| language | English |
| last_indexed | 2024-12-14T20:10:03Z |
| publishDate | 2021-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of King Saud University: Science |
| spelling | doaj.art-d33bc245fa1e4d08b5fc688dfd24ab7e2022-12-21T22:48:57ZengElsevierJournal of King Saud University: Science1018-36472021-01-01331101275Analysis of a fractional-order chaotic system in the context of the Caputo fractional derivative via bifurcation and Lyapunov exponentsNdolane Sene0Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Faculté des Sciences Economiques et Gestion, BP 5683 Dakar Fann, SenegalThis research focuses on the characterization of the chaotic behaviors, the hyperchaotic behaviors, and the impact of the fractional-order derivative in a class of fractional chaotic system. The numerical scheme, including the discretization of the Riemann–Liouville derivative, will be used to depict the phase portraits of the fractional-order chaotic system when the order of the used fractional-order derivative takes different values. The impact of the fractional-order derivative in the fractional chaotic system will be investigated. The proposed numerical scheme proposes a new alternative to obtain the phase portraits of the fractional-order chaotic systems. The sensitivity of the chaotic systems to the changes in the initial condition and the variation of the parameters of the considered model will be focussed with precision using the bifurcation diagrams and the Lyapunov exponent. The stability of the equilibrium points of the commensurable fractional-order chaotic system will be addressed in the context of fractional calculus. In other words, we will use the standard Matignon criterion to address the problem of stability. The main attraction and novelty of this paper will be the use of the Lyapunov exponent to characterize the nature of chaos and to prove the dissipativity of the considered chaotic system.http://www.sciencedirect.com/science/article/pii/S1018364720303888BifurcationLyapunov exponentChaotic systems |
| spellingShingle | Ndolane Sene Analysis of a fractional-order chaotic system in the context of the Caputo fractional derivative via bifurcation and Lyapunov exponents Journal of King Saud University: Science Bifurcation Lyapunov exponent Chaotic systems |
| title | Analysis of a fractional-order chaotic system in the context of the Caputo fractional derivative via bifurcation and Lyapunov exponents |
| title_full | Analysis of a fractional-order chaotic system in the context of the Caputo fractional derivative via bifurcation and Lyapunov exponents |
| title_fullStr | Analysis of a fractional-order chaotic system in the context of the Caputo fractional derivative via bifurcation and Lyapunov exponents |
| title_full_unstemmed | Analysis of a fractional-order chaotic system in the context of the Caputo fractional derivative via bifurcation and Lyapunov exponents |
| title_short | Analysis of a fractional-order chaotic system in the context of the Caputo fractional derivative via bifurcation and Lyapunov exponents |
| title_sort | analysis of a fractional order chaotic system in the context of the caputo fractional derivative via bifurcation and lyapunov exponents |
| topic | Bifurcation Lyapunov exponent Chaotic systems |
| url | http://www.sciencedirect.com/science/article/pii/S1018364720303888 |
| work_keys_str_mv | AT ndolanesene analysisofafractionalorderchaoticsysteminthecontextofthecaputofractionalderivativeviabifurcationandlyapunovexponents |