Chaotic Map with No Fixed Points: Entropy, Implementation and Control

A map without equilibrium has been proposed and studied in this paper. The proposed map has no fixed point and exhibits chaos. We have investigated its dynamics and shown its chaotic behavior using tools such as return map, bifurcation diagram and Lyapunov exponents’ diagram. Entropy of this new map...

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Detalles Bibliográficos
Autores principales: Huynh, Van Van, Ouannas, Adel, Wang, Xiong, Pham, Viet-Thanh, Nguyen, Xuan Quynh, Alsaadi, Fawaz E.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514759/
https://www.ncbi.nlm.nih.gov/pubmed/33266994
http://dx.doi.org/10.3390/e21030279
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author Huynh, Van Van
Ouannas, Adel
Wang, Xiong
Pham, Viet-Thanh
Nguyen, Xuan Quynh
Alsaadi, Fawaz E.
author_facet Huynh, Van Van
Ouannas, Adel
Wang, Xiong
Pham, Viet-Thanh
Nguyen, Xuan Quynh
Alsaadi, Fawaz E.
author_sort Huynh, Van Van
collection PubMed
description A map without equilibrium has been proposed and studied in this paper. The proposed map has no fixed point and exhibits chaos. We have investigated its dynamics and shown its chaotic behavior using tools such as return map, bifurcation diagram and Lyapunov exponents’ diagram. Entropy of this new map has been calculated. Using an open micro-controller platform, the map is implemented, and experimental observation is presented. In addition, two control schemes have been proposed to stabilize and synchronize the chaotic map.
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spelling pubmed-75147592020-11-09 Chaotic Map with No Fixed Points: Entropy, Implementation and Control Huynh, Van Van Ouannas, Adel Wang, Xiong Pham, Viet-Thanh Nguyen, Xuan Quynh Alsaadi, Fawaz E. Entropy (Basel) Article A map without equilibrium has been proposed and studied in this paper. The proposed map has no fixed point and exhibits chaos. We have investigated its dynamics and shown its chaotic behavior using tools such as return map, bifurcation diagram and Lyapunov exponents’ diagram. Entropy of this new map has been calculated. Using an open micro-controller platform, the map is implemented, and experimental observation is presented. In addition, two control schemes have been proposed to stabilize and synchronize the chaotic map. MDPI 2019-03-14 /pmc/articles/PMC7514759/ /pubmed/33266994 http://dx.doi.org/10.3390/e21030279 Text en © 2019 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
Huynh, Van Van
Ouannas, Adel
Wang, Xiong
Pham, Viet-Thanh
Nguyen, Xuan Quynh
Alsaadi, Fawaz E.
Chaotic Map with No Fixed Points: Entropy, Implementation and Control
title Chaotic Map with No Fixed Points: Entropy, Implementation and Control
title_full Chaotic Map with No Fixed Points: Entropy, Implementation and Control
title_fullStr Chaotic Map with No Fixed Points: Entropy, Implementation and Control
title_full_unstemmed Chaotic Map with No Fixed Points: Entropy, Implementation and Control
title_short Chaotic Map with No Fixed Points: Entropy, Implementation and Control
title_sort chaotic map with no fixed points: entropy, implementation and control
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514759/
https://www.ncbi.nlm.nih.gov/pubmed/33266994
http://dx.doi.org/10.3390/e21030279
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