On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization

In this paper, we propose a fractional map based on the integer-order unified map. The chaotic behavior of the proposed map is analyzed by means of bifurcations plots, and experimental bounds are placed on the parameters and fractional order. Different control laws are proposed to force the states t...

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Detalles Bibliográficos
Autores principales: Khennaoui, Amina-Aicha, Ouannas, Adel, Bendoukha, Samir, Wang, Xiong, Pham, Viet-Thanh
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7513057/
https://www.ncbi.nlm.nih.gov/pubmed/33265619
http://dx.doi.org/10.3390/e20070530
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author Khennaoui, Amina-Aicha
Ouannas, Adel
Bendoukha, Samir
Wang, Xiong
Pham, Viet-Thanh
author_facet Khennaoui, Amina-Aicha
Ouannas, Adel
Bendoukha, Samir
Wang, Xiong
Pham, Viet-Thanh
author_sort Khennaoui, Amina-Aicha
collection PubMed
description In this paper, we propose a fractional map based on the integer-order unified map. The chaotic behavior of the proposed map is analyzed by means of bifurcations plots, and experimental bounds are placed on the parameters and fractional order. Different control laws are proposed to force the states to zero asymptotically and to achieve the complete synchronization of a pair of fractional unified maps with identical or nonidentical parameters. Numerical results are used throughout the paper to illustrate the findings.
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spelling pubmed-75130572020-11-09 On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization Khennaoui, Amina-Aicha Ouannas, Adel Bendoukha, Samir Wang, Xiong Pham, Viet-Thanh Entropy (Basel) Article In this paper, we propose a fractional map based on the integer-order unified map. The chaotic behavior of the proposed map is analyzed by means of bifurcations plots, and experimental bounds are placed on the parameters and fractional order. Different control laws are proposed to force the states to zero asymptotically and to achieve the complete synchronization of a pair of fractional unified maps with identical or nonidentical parameters. Numerical results are used throughout the paper to illustrate the findings. MDPI 2018-07-15 /pmc/articles/PMC7513057/ /pubmed/33265619 http://dx.doi.org/10.3390/e20070530 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Khennaoui, Amina-Aicha
Ouannas, Adel
Bendoukha, Samir
Wang, Xiong
Pham, Viet-Thanh
On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization
title On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization
title_full On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization
title_fullStr On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization
title_full_unstemmed On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization
title_short On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization
title_sort on chaos in the fractional-order discrete-time unified system and its control synchronization
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7513057/
https://www.ncbi.nlm.nih.gov/pubmed/33265619
http://dx.doi.org/10.3390/e20070530
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