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...
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doaj-ba8aea0d01784f998ff592118c4f525c2020-11-24T21:45:39ZengMDPI AGApplied Sciences2076-34172018-12-01812264010.3390/app8122640app8122640The Fractional Form of the Tinkerbell Map Is ChaoticAdel Ouannas0Amina-Aicha Khennaoui1Samir Bendoukha2Thoai Phu Vo3Viet-Thanh Pham4Van Van Huynh5Department of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa 12002, AlgeriaDepartment of Mathematics and Computer Sciences, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, AlgeriaElectrical Engineering Department, College of Engineering at Yanbu, Taibah University, Medina 42353, Saudi ArabiaFaculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, VietnamNonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, VietnamModeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, VietnamThis 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.https://www.mdpi.com/2076-3417/8/12/2640fractional discrete calculusdiscrete chaosTinkerbell mapbifurcationstabilization |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Adel Ouannas Amina-Aicha Khennaoui Samir Bendoukha Thoai Phu Vo Viet-Thanh Pham Van Van Huynh |
spellingShingle |
Adel Ouannas Amina-Aicha Khennaoui Samir Bendoukha Thoai Phu Vo Viet-Thanh Pham Van Van Huynh The Fractional Form of the Tinkerbell Map Is Chaotic Applied Sciences fractional discrete calculus discrete chaos Tinkerbell map bifurcation stabilization |
author_facet |
Adel Ouannas Amina-Aicha Khennaoui Samir Bendoukha Thoai Phu Vo Viet-Thanh Pham Van Van Huynh |
author_sort |
Adel Ouannas |
title |
The Fractional Form of the Tinkerbell Map Is Chaotic |
title_short |
The Fractional Form of the Tinkerbell Map Is Chaotic |
title_full |
The Fractional Form of the Tinkerbell Map Is Chaotic |
title_fullStr |
The Fractional Form of the Tinkerbell Map Is Chaotic |
title_full_unstemmed |
The Fractional Form of the Tinkerbell Map Is Chaotic |
title_sort |
fractional form of the tinkerbell map is chaotic |
publisher |
MDPI AG |
series |
Applied Sciences |
issn |
2076-3417 |
publishDate |
2018-12-01 |
description |
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. |
topic |
fractional discrete calculus discrete chaos Tinkerbell map bifurcation stabilization |
url |
https://www.mdpi.com/2076-3417/8/12/2640 |
work_keys_str_mv |
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