The Fractional Form of the Tinkerbell Map Is Chaotic

This paper is concerned with a fractional Caputo-difference form of the well-known Tinkerbell chaotic map. The dynamics of the proposed map are investigated numerically through phase plots, bifurcation diagrams, and Lyapunov exponents considered from different perspectives. In addition, a stabilizat...

Full description

Saved in:
Bibliographic Details
Published inApplied sciences Vol. 8; no. 12; p. 2640
Main Authors Ouannas, Adel, Khennaoui, Amina-Aicha, Bendoukha, Samir, Vo, Thoai, Pham, Viet-Thanh, Huynh, Van
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2018
Subjects
Asymptotic properties
bifurcation
Calculus
Control theory
Data encryption
discrete chaos
Discrete systems
Dynamical systems
Engineering
Film adaptations
fractional discrete calculus
stabilization
Tinkerbell map
Vietnam
Algeria
Online AccessGet full text

Cover

More Information
Summary:This paper is concerned with a fractional Caputo-difference form of the well-known Tinkerbell chaotic map. The dynamics of the proposed map are investigated numerically through phase plots, bifurcation diagrams, and Lyapunov exponents considered from different perspectives. In addition, a stabilization controller is proposed, and the asymptotic convergence of the states is established by means of the stability theory of linear fractional discrete systems. Numerical results are employed to confirm the analytical findings.
ISSN:2076-3417
2076-3417
DOI:10.3390/app8122640