On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative
Joint Authors
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-17
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Sene, Ndolane& Ndiaye, Ameth. 2020. On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative. Journal of Mathematics،Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1188214
Modern Language Association (MLA)
Sene, Ndolane& Ndiaye, Ameth. On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative. Journal of Mathematics No. 2020 (2020), pp.1-15.
https://search.emarefa.net/detail/BIM-1188214
American Medical Association (AMA)
Sene, Ndolane& Ndiaye, Ameth. On Class of Fractional-Order Chaotic or Hyperchaotic Systems in the Context of the Caputo Fractional-Order Derivative. Journal of Mathematics. 2020. Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1188214
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1188214