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 th...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-03-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/21/3/279 |
| _version_ | 1798035341094944768 |
|---|---|
| author | Van Van Huynh Adel Ouannas Xiong Wang Viet-Thanh Pham Xuan Quynh Nguyen Fawaz E. Alsaadi |
| author_facet | Van Van Huynh Adel Ouannas Xiong Wang Viet-Thanh Pham Xuan Quynh Nguyen Fawaz E. Alsaadi |
| author_sort | Van Van Huynh |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T20:56:53Z |
| format | Article |
| id | doaj.art-ce81a318ad064e32924213fca9ff2d89 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T20:56:53Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-ce81a318ad064e32924213fca9ff2d892022-12-22T04:03:40ZengMDPI AGEntropy1099-43002019-03-0121327910.3390/e21030279e21030279Chaotic Map with No Fixed Points: Entropy, Implementation and ControlVan Van Huynh0Adel Ouannas1Xiong Wang2Viet-Thanh Pham3Xuan Quynh Nguyen4Fawaz E. Alsaadi5Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, VietnamDepartment of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa 12002, AlgeriaInstitute for Advanced Study, Shenzhen University, Shenzhen 518060, ChinaNonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, VietnamNational Council for Science and Technology Policy, Hanoi, VietnamDepartment of Information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah 21589, Saudi ArabiaA 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.http://www.mdpi.com/1099-4300/21/3/279chaotic mapfixed pointchaosapproximate entropyimplementation |
| spellingShingle | Van Van Huynh Adel Ouannas Xiong Wang Viet-Thanh Pham Xuan Quynh Nguyen Fawaz E. Alsaadi Chaotic Map with No Fixed Points: Entropy, Implementation and Control Entropy chaotic map fixed point chaos approximate entropy implementation |
| 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 | chaotic map fixed point chaos approximate entropy implementation |
| url | http://www.mdpi.com/1099-4300/21/3/279 |
| work_keys_str_mv | AT vanvanhuynh chaoticmapwithnofixedpointsentropyimplementationandcontrol AT adelouannas chaoticmapwithnofixedpointsentropyimplementationandcontrol AT xiongwang chaoticmapwithnofixedpointsentropyimplementationandcontrol AT vietthanhpham chaoticmapwithnofixedpointsentropyimplementationandcontrol AT xuanquynhnguyen chaoticmapwithnofixedpointsentropyimplementationandcontrol AT fawazealsaadi chaoticmapwithnofixedpointsentropyimplementationandcontrol |