{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T22:43:03Z","timestamp":1773787383750,"version":"3.50.1"},"reference-count":60,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T00:00:00Z","timestamp":1678665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Mexican Research Council: Consejo Nacional de Ciencia y Tecnolog\u00eda (CONACYT)","doi-asserted-by":"publisher","award":["731641"],"award-info":[{"award-number":["731641"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003141","name":"Mexican Research Council: Consejo Nacional de Ciencia y Tecnolog\u00eda (CONACYT)","doi-asserted-by":"publisher","award":["C127.10028. 65661"],"award-info":[{"award-number":["C127.10028. 65661"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000855","name":"University of Birmingham","doi-asserted-by":"publisher","award":["731641"],"award-info":[{"award-number":["731641"]}],"id":[{"id":"10.13039\/501100000855","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000855","name":"University of Birmingham","doi-asserted-by":"publisher","award":["C127.10028. 65661"],"award-info":[{"award-number":["C127.10028. 65661"]}],"id":[{"id":"10.13039\/501100000855","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi\u2013Sugeno (T\u2013S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.<\/jats:p>","DOI":"10.3390\/e25030495","type":"journal-article","created":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T03:04:46Z","timestamp":1678763086000},"page":"495","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Fuzzy Synchronization of Chaotic Systems with Hidden Attractors"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0736-8820","authenticated-orcid":false,"given":"Jessica","family":"Zaqueros-Martinez","sequence":"first","affiliation":[{"name":"Department of Computer Science, Instituto Nacional de Astrof\u00edsica, \u00d3ptica y Electr\u00f3nica (INAOE), Tonantzintla, Puebla 72840, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4925-8892","authenticated-orcid":false,"given":"Gustavo","family":"Rodriguez-Gomez","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Instituto Nacional de Astrof\u00edsica, \u00d3ptica y Electr\u00f3nica (INAOE), Tonantzintla, Puebla 72840, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7187-4686","authenticated-orcid":false,"given":"Esteban","family":"Tlelo-Cuautle","sequence":"additional","affiliation":[{"name":"Department of Electronics, Instituto Nacional de Astrof\u00edsica, \u00d3ptica y Electr\u00f3nica (INAOE), Tonantzintla, Puebla 72840, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8963-7283","authenticated-orcid":false,"given":"Felipe","family":"Orihuela-Espina","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Instituto Nacional de Astrof\u00edsica, \u00d3ptica y Electr\u00f3nica (INAOE), Tonantzintla, Puebla 72840, Mexico"},{"name":"School of Computer Science, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2211","DOI":"10.1007\/s12555-018-0216-5","article-title":"Synchronization of Fractional Hyperchaotic Rabinovich Systems via Linear and Nonlinear Control with an Application to Secure Communications","volume":"17","author":"Ouannas","year":"2019","journal-title":"Int. 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