On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative
In this paper, we consider a class of fractional-order systems described by the Caputo derivative. The behaviors of the dynamics of this particular class of fractional-order systems will be proposed and experienced by a numerical scheme to obtain the phase portraits. Before that, we will provide the...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8815377 |
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| author | Ndolane Sene Ameth Ndiaye |
| author_facet | Ndolane Sene Ameth Ndiaye |
| author_sort | Ndolane Sene |
| collection | DOAJ |
| description | In this paper, we consider a class of fractional-order systems described by the Caputo derivative. The behaviors of the dynamics of this particular class of fractional-order systems will be proposed and experienced by a numerical scheme to obtain the phase portraits. Before that, we will provide the conditions under which the considered fractional-order system’s solution exists and is unique. The fractional-order impact will be analyzed, and the advantages of the fractional-order derivatives in modeling chaotic systems will be discussed. How the parameters of the model influence the considered fractional-order system will be studied using the Lyapunov exponents. The topological changes of the systems and the detection of the chaotic and hyperchaotic behaviors at the assumed initial conditions and the considered fractional-order systems will also be investigated using the Lyapunov exponents. The investigations related to the Lyapunov exponents in the context of the fractional-order derivative will be the main novelty of this paper. The stability analysis of the model’s equilibrium points has been focused in terms of the Matignon criterion. |
| format | Article |
| id | doaj-art-2b48e54d45284dda9d697236a8685b94 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-2b48e54d45284dda9d697236a8685b942025-02-03T01:20:21ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/88153778815377On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order DerivativeNdolane Sene0Ameth Ndiaye1Laboratoire Lmdan, Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Faculté des Sciences Economiques et Gestion, Dakar Fann BP 5683, SenegalDépartement de Mathématiques, Faculté des Sciences et Technologies de L’Education et de la Formation, Université Cheikh Anta Diop de Dakar, BP 5036 Dakar Fann, SenegalIn this paper, we consider a class of fractional-order systems described by the Caputo derivative. The behaviors of the dynamics of this particular class of fractional-order systems will be proposed and experienced by a numerical scheme to obtain the phase portraits. Before that, we will provide the conditions under which the considered fractional-order system’s solution exists and is unique. The fractional-order impact will be analyzed, and the advantages of the fractional-order derivatives in modeling chaotic systems will be discussed. How the parameters of the model influence the considered fractional-order system will be studied using the Lyapunov exponents. The topological changes of the systems and the detection of the chaotic and hyperchaotic behaviors at the assumed initial conditions and the considered fractional-order systems will also be investigated using the Lyapunov exponents. The investigations related to the Lyapunov exponents in the context of the fractional-order derivative will be the main novelty of this paper. The stability analysis of the model’s equilibrium points has been focused in terms of the Matignon criterion.http://dx.doi.org/10.1155/2020/8815377 |
| spellingShingle | Ndolane Sene Ameth Ndiaye On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative Journal of Mathematics |
| title | On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative |
| title_full | On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative |
| title_fullStr | On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative |
| title_full_unstemmed | On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative |
| title_short | On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative |
| title_sort | on class of fractional order chaotic or hyperchaotic systems in the context of the caputo fractional order derivative |
| url | http://dx.doi.org/10.1155/2020/8815377 |
| work_keys_str_mv | AT ndolanesene onclassoffractionalorderchaoticorhyperchaoticsystemsinthecontextofthecaputofractionalorderderivative AT amethndiaye onclassoffractionalorderchaoticorhyperchaoticsystemsinthecontextofthecaputofractionalorderderivative |