Study of a Fractional-Order Chaotic System Represented by the Caputo Operator
This paper is presented on the theory and applications of the fractional-order chaotic system described by the Caputo fractional derivative. Considering the new fractional model, it is important to establish the presence or absence of chaotic behaviors. The Lyapunov exponents in the fractional conte...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/5534872 |
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| _version_ | 1832561532792209408 |
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| author | Ndolane Sene |
| author_facet | Ndolane Sene |
| author_sort | Ndolane Sene |
| collection | DOAJ |
| description | This paper is presented on the theory and applications of the fractional-order chaotic system described by the Caputo fractional derivative. Considering the new fractional model, it is important to establish the presence or absence of chaotic behaviors. The Lyapunov exponents in the fractional context will be our fundamental tool to arrive at our conclusions. The variations of the model’s parameters will generate chaotic behavior, in general, which will be established using the Lyapunov exponents and bifurcation diagrams. For the system’s phase portrait, we will present and apply an interesting fractional numerical discretization. For confirmation of the results provided in this paper, the circuit schematic is drawn and simulated. As it will be observed, the results obtained after the simulation of the numerical scheme and with the Multisim are in good agreement. |
| format | Article |
| id | doaj-art-dad2afd96ebb4b4aa3e422a2f51f7c0b |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-dad2afd96ebb4b4aa3e422a2f51f7c0b2025-02-03T01:24:49ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/55348725534872Study of a Fractional-Order Chaotic System Represented by the Caputo OperatorNdolane Sene0Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Faculté des Sciences Economiques et Gestion, BP 5683 Dakar Fann, SenegalThis paper is presented on the theory and applications of the fractional-order chaotic system described by the Caputo fractional derivative. Considering the new fractional model, it is important to establish the presence or absence of chaotic behaviors. The Lyapunov exponents in the fractional context will be our fundamental tool to arrive at our conclusions. The variations of the model’s parameters will generate chaotic behavior, in general, which will be established using the Lyapunov exponents and bifurcation diagrams. For the system’s phase portrait, we will present and apply an interesting fractional numerical discretization. For confirmation of the results provided in this paper, the circuit schematic is drawn and simulated. As it will be observed, the results obtained after the simulation of the numerical scheme and with the Multisim are in good agreement.http://dx.doi.org/10.1155/2021/5534872 |
| spellingShingle | Ndolane Sene Study of a Fractional-Order Chaotic System Represented by the Caputo Operator Complexity |
| title | Study of a Fractional-Order Chaotic System Represented by the Caputo Operator |
| title_full | Study of a Fractional-Order Chaotic System Represented by the Caputo Operator |
| title_fullStr | Study of a Fractional-Order Chaotic System Represented by the Caputo Operator |
| title_full_unstemmed | Study of a Fractional-Order Chaotic System Represented by the Caputo Operator |
| title_short | Study of a Fractional-Order Chaotic System Represented by the Caputo Operator |
| title_sort | study of a fractional order chaotic system represented by the caputo operator |
| url | http://dx.doi.org/10.1155/2021/5534872 |
| work_keys_str_mv | AT ndolanesene studyofafractionalorderchaoticsystemrepresentedbythecaputooperator |