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Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems

This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behavio...

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Autores principales: Debbouche, Nadjette, Momani, Shaher, Ouannas, Adel, Shatnawi, ’Mohd Taib’, Grassi, Giuseppe, Dibi, Zohir, Batiha, Iqbal M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7995993/
https://www.ncbi.nlm.nih.gov/pubmed/33668123
http://dx.doi.org/10.3390/e23030261
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author Debbouche, Nadjette
Momani, Shaher
Ouannas, Adel
Shatnawi, ’Mohd Taib’
Grassi, Giuseppe
Dibi, Zohir
Batiha, Iqbal M.
author_facet Debbouche, Nadjette
Momani, Shaher
Ouannas, Adel
Shatnawi, ’Mohd Taib’
Grassi, Giuseppe
Dibi, Zohir
Batiha, Iqbal M.
author_sort Debbouche, Nadjette
collection PubMed
description This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.
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spelling pubmed-79959932021-03-27 Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems Debbouche, Nadjette Momani, Shaher Ouannas, Adel Shatnawi, ’Mohd Taib’ Grassi, Giuseppe Dibi, Zohir Batiha, Iqbal M. Entropy (Basel) Article This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results. MDPI 2021-02-24 /pmc/articles/PMC7995993/ /pubmed/33668123 http://dx.doi.org/10.3390/e23030261 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/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/ (https://creativecommons.org/licenses/by/4.0/) ).
spellingShingle Article
Debbouche, Nadjette
Momani, Shaher
Ouannas, Adel
Shatnawi, ’Mohd Taib’
Grassi, Giuseppe
Dibi, Zohir
Batiha, Iqbal M.
Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems
title Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems
title_full Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems
title_fullStr Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems
title_full_unstemmed Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems
title_short Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems
title_sort generating multidirectional variable hidden attractors via newly commensurate and incommensurate non-equilibrium fractional-order chaotic systems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7995993/
https://www.ncbi.nlm.nih.gov/pubmed/33668123
http://dx.doi.org/10.3390/e23030261
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