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Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control

This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1...

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Detalles Bibliográficos
Autores principales: Almatroud, A. Othman, Khennaoui, Amina-Aicha, Ouannas, Adel, Grassi, Giuseppe, Al-sawalha, M. Mossa, Gasri, Ahlem
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7759845/
https://www.ncbi.nlm.nih.gov/pubmed/33266528
http://dx.doi.org/10.3390/e22121344
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author Almatroud, A. Othman
Khennaoui, Amina-Aicha
Ouannas, Adel
Grassi, Giuseppe
Al-sawalha, M. Mossa
Gasri, Ahlem
author_facet Almatroud, A. Othman
Khennaoui, Amina-Aicha
Ouannas, Adel
Grassi, Giuseppe
Al-sawalha, M. Mossa
Gasri, Ahlem
author_sort Almatroud, A. Othman
collection PubMed
description This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.
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spelling pubmed-77598452021-02-24 Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control Almatroud, A. Othman Khennaoui, Amina-Aicha Ouannas, Adel Grassi, Giuseppe Al-sawalha, M. Mossa Gasri, Ahlem Entropy (Basel) Article This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package. MDPI 2020-11-27 /pmc/articles/PMC7759845/ /pubmed/33266528 http://dx.doi.org/10.3390/e22121344 Text en © 2020 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
Almatroud, A. Othman
Khennaoui, Amina-Aicha
Ouannas, Adel
Grassi, Giuseppe
Al-sawalha, M. Mossa
Gasri, Ahlem
Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control
title Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control
title_full Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control
title_fullStr Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control
title_full_unstemmed Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control
title_short Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control
title_sort dynamical analysis of a new chaotic fractional discrete-time system and its control
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7759845/
https://www.ncbi.nlm.nih.gov/pubmed/33266528
http://dx.doi.org/10.3390/e22121344
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