{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:27:25Z","timestamp":1764174445201,"version":"build-2065373602"},"reference-count":96,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,1,27]],"date-time":"2018-01-27T00:00:00Z","timestamp":1517011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we introduce a new chaotic system that is used for an engineering application of the signal encryption. It has some interesting features, and its successful implementation and manufacturing were performed via a real circuit as a random number generator. In addition, we provide a parameter estimation method to extract chaotic model parameters from the real data of the chaotic circuit. The parameter estimation method is based on the attractor distribution modeling in the state space, which is compatible with the chaotic system characteristics. Here, a Gaussian mixture model (GMM) is used as a main part of cost function computations in the parameter estimation method. To optimize the cost function, we also apply two recent efficient optimization methods: WOA (Whale Optimization Algorithm), and MVO (Multi-Verse Optimizer) algorithms. The results show the success of the parameter estimation procedure.<\/jats:p>","DOI":"10.3390\/e20020086","type":"journal-article","created":{"date-parts":[[2018,1,29]],"date-time":"2018-01-29T07:46:20Z","timestamp":1517211980000},"page":"86","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":81,"title":["A New Chaotic System with a Self-Excited Attractor: Entropy Measurement, Signal Encryption, and Parameter Estimation"],"prefix":"10.3390","volume":"20","author":[{"given":"Guanghui","family":"Xu","sequence":"first","affiliation":[{"name":"School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan 430068, China"},{"name":"Hubei Collaborative Innovation Center for High-efficiency Utilization of Solar Energy, Hubei University of Technology, Wuhan 430068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6733-3702","authenticated-orcid":false,"given":"Yasser","family":"Shekofteh","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science and Engineering, Shahid Beheshti University, Tehran 1983969411, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akif","family":"Akg\u00fcl","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Faculty of Technology, Sakarya University, Serdivan 54187, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunbiao","family":"Li","sequence":"additional","affiliation":[{"name":"Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science &amp; Technology, Nanjing 210044, China"},{"name":"School of Electronic &amp; Information Engineering, Nanjing University of Information Science &amp; Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shirin","family":"Panahi","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, Amirkabir University of Technology, Tehran 1591634311, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"10389","DOI":"10.1016\/j.ijleo.2016.08.046","article-title":"Variable-boostable chaotic flows","volume":"127","author":"Li","year":"2016","journal-title":"Opt.-Int. 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