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Entropy 2019, 21(3), 279; https://doi.org/10.3390/e21030279

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

1
Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
2
Department of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa 12002, Algeria
3
Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
4
Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
5
National Council for Science and Technology Policy, Hanoi, Vietnam
6
Department of Information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah 21589, Saudi Arabia
*
Author to whom correspondence should be addressed.
Received: 29 January 2019 / Revised: 7 March 2019 / Accepted: 12 March 2019 / Published: 14 March 2019
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Abstract

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. View Full-Text
Keywords: chaotic map; fixed point; chaos; approximate entropy; implementation chaotic map; fixed point; chaos; approximate entropy; implementation
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Huynh, V.V.; Ouannas, A.; Wang, X.; Pham, V.-T.; Nguyen, X.Q.; Alsaadi, F.E. Chaotic Map with No Fixed Points: Entropy, Implementation and Control. Entropy 2019, 21, 279.

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