{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:34:08Z","timestamp":1760783648544,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2013,2,18]],"date-time":"2013-02-18T00:00:00Z","timestamp":1361145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents the synchronization between the master and slave Lorenz chaotic systems by slide mode controller (SMC)-based technique. A proportional-integral (PI) switching surface is proposed to simplify the task of assigning the performance of the closed-loop error system in sliding mode. Then, extending the concept of equivalent control and using some basic electronic components, a secure communication system is constructed. Experimental results show the feasibility of synchronizing two Lorenz circuits via the proposed SMC.<\/jats:p>","DOI":"10.3390\/s130202494","type":"journal-article","created":{"date-parts":[[2013,2,19]],"date-time":"2013-02-19T11:11:16Z","timestamp":1361272276000},"page":"2494-2505","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Hardware Implementation of Lorenz Circuit Systems for  Secure Chaotic Communication Applications"],"prefix":"10.3390","volume":"13","author":[{"given":"Hsin-Chieh","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Biomedical Engineering, Hungkuang University, Taichung 43302, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ben-Yi","family":"Liau","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, Hungkuang University, Taichung 43302, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi-You","family":"Hou","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Far East University, Tainan 74448, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,2,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","article-title":"Deterministic non-periodic flows","volume":"20","author":"Lorenz","year":"1963","journal-title":"J. Atmos. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1103\/PhysRevLett.64.821","article-title":"Synchronization in chaotic systems","volume":"64","author":"Pecora","year":"1990","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1016\/j.chaos.2004.05.001","article-title":"Implementation of chaotic secure communication systems based on OPA circuits","volume":"23","author":"Huang","year":"2005","journal-title":"Chaos Solitons Fractals"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.physleta.2005.07.083","article-title":"Security analysis of communication system based on the synchronization of different order chaotic systems","volume":"345","author":"Alvarez","year":"2005","journal-title":"Phys. Lett. A."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1515\/IJNSNS.2006.7.3.333","article-title":"Fuzzy sliding mode control for a class of chaos synchronization with uncertainties","volume":"7","author":"Yau","year":"2006","journal-title":"Int. J. Nonlin. Sci. Num. Simul."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1142\/S0218127408020264","article-title":"Chaotic synchronization and secure communication via sliding-mode observer","volume":"18","author":"Yu","year":"2008","journal-title":"Int. J. Bifurcat. Chaos."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1016\/j.nonrwa.2007.03.005","article-title":"Adaptive feedback controller for projective synchronization","volume":"9","author":"Hu","year":"2008","journal-title":"Nonlin. Anal. Real World Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1016\/S0960-0779(99)00051-X","article-title":"Adaptive synchronization of chaotic systems and its application to secure communications","volume":"11","author":"Liao","year":"2000","journal-title":"Chaos Solitons Fractals"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1306","DOI":"10.1109\/TCOMM.2003.815058","article-title":"A new chaotic secure communication system","volume":"51","author":"Li","year":"2003","journal-title":"IEEE Trans. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Li, Z., and Xu, D. (2004). A secure communication scheme using projective chaos synchronization. Chaos Solitons Fractals, 477\u2013481.","DOI":"10.1016\/j.chaos.2004.02.019"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.chaos.2005.09.011","article-title":"Robust synchronization of Sprott circuits using sliding mode control","volume":"30","author":"Almeida","year":"2006","journal-title":"Chaos Solitons Fractals"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.physleta.2004.12.071","article-title":"Communication with spatial periodic chaos synchronization","volume":"335","author":"Zhou","year":"2005","journal-title":"Phys. Lett. A."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1142","DOI":"10.1016\/j.chaos.2005.08.078","article-title":"Synthesis for robust synchronization of chaotic systems under output feedback control with multiple random delays","volume":"29","author":"Wen","year":"2006","journal-title":"Chaos Solitons Fractals"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Hou, Y.Y., Liau, B.Y., and Chen, H.C. (2012). Synchronization of unified chaotic systems using sliding mode controller. Math. Probl. Eng.","DOI":"10.1155\/2012\/632712"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1815","DOI":"10.1016\/S0005-1098(02)00098-5","article-title":"Sliding mode observers for detection and reconstruction of sensor faults","volume":"38","author":"Tan","year":"2002","journal-title":"Automatica"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/S0005-1098(99)00177-6","article-title":"Sliding mode observers for fault detection and isolation","volume":"36","author":"Edwards","year":"2000","journal-title":"Automatica"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/2\/2494\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:45:01Z","timestamp":1760219101000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/2\/2494"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,18]]},"references-count":16,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,2]]}},"alternative-id":["s130202494"],"URL":"https:\/\/doi.org\/10.3390\/s130202494","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2013,2,18]]}}}