{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T15:38:41Z","timestamp":1776008321064,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,14]],"date-time":"2019-03-14T00:00:00Z","timestamp":1552521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 61601306"],"award-info":[{"award-number":["No. 61601306"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shenzhen Overseas High Level Talent Peacock Project Fund","award":["No. 20150215145C"],"award-info":[{"award-number":["No. 20150215145C"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2019 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.<\/jats:p>","DOI":"10.3390\/e21030279","type":"journal-article","created":{"date-parts":[[2019,3,15]],"date-time":"2019-03-15T04:12:09Z","timestamp":1552623129000},"page":"279","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":46,"title":["Chaotic Map with No Fixed Points: Entropy, Implementation and Control"],"prefix":"10.3390","volume":"21","author":[{"given":"Van Van","family":"Huynh","sequence":"first","affiliation":[{"name":"Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adel","family":"Ouannas","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa 12002, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiong","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Viet-Thanh","family":"Pham","sequence":"additional","affiliation":[{"name":"Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuan Quynh","family":"Nguyen","sequence":"additional","affiliation":[{"name":"National Council for Science and Technology Policy, Hanoi, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0041-3158","authenticated-orcid":false,"given":"Fawaz E.","family":"Alsaadi","sequence":"additional","affiliation":[{"name":"Department of Information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,14]]},"reference":[{"key":"ref_1","unstructured":"Pierre, C., and Jean-Pierre, E. 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