The Discrete Fractional Variable-Order Tinkerbell Map: Chaos, 0–1 Test, and Entropy

Souad Bensid Ahmed (), Adel Ouannas, Mohammed Al Horani and Giuseppe Grassi
Additional contact information
Souad Bensid Ahmed: Departement of Mathematics, The University of Jordan, Amman 11942, Jordan
Adel Ouannas: Departement of Mathematics and Computer Science, The University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Mohammed Al Horani: Departement of Mathematics, The University of Jordan, Amman 11942, Jordan
Giuseppe Grassi: Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy

Mathematics, 2022, vol. 10, issue 17, 1-13

Abstract: The dynamics of the Caputo-fractional variable-order difference form of the Tinkerbell map are studied. The phase portraits, bifurcation, and largest Lyapunov exponent (LLE) were employed to demonstrate the presence of chaos over a different fractional variable-order and establish the nature of the dynamics. In addition, the 0–1 test tool was used to detect chaos. Finally, the numerical results were confirmed using the approximate entropy.

Keywords: fractional variable-order; Tinkerbell map; chaos; bifurcation; Lyapunov exponents; 0–1 test; approximate entropy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/17/3173/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/17/3173/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:17:p:3173-:d:905733

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().