{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:06:19Z","timestamp":1760234779961,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T00:00:00Z","timestamp":1623196800000},"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":["61871230"],"award-info":[{"award-number":["61871230"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20181410"],"award-info":[{"award-number":["BK20181410"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Major Program of Natural Science Foundation of Shandong Province","award":["ZR2020KA007"],"award-info":[{"award-number":["ZR2020KA007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Trigonometric functions were used to construct a 2-D symmetrical hyperchaotic map with infinitely many attractors. The regime of multistability depends on the periodicity of the trigonometric function, which is closely related to the initial condition. For this trigonometric nonlinearity and the introduction of an offset controller, the initial condition triggers a specific multistability evolvement, in which infinitely countless symmetric and asymmetric attractors are produced. Initial condition-triggered offset boosting is explored, combined with constant controlled offset regulation. Furthermore, this symmetric map gives the sequences in various types of asymmetric attractors, in which the polarity balance is maintained by the initial condition and a negative coefficient due to the trigonometric function. Finally, as determined through the hardware implementation of STM32, the corresponding results agree with the numerical simulation.<\/jats:p>","DOI":"10.3390\/sym13061039","type":"journal-article","created":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T04:22:22Z","timestamp":1623212542000},"page":"1039","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Asymmetry Evolvement and Controllability of a Symmetric Hyperchaotic Map"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3607-9673","authenticated-orcid":false,"given":"Sixiao","family":"Kong","sequence":"first","affiliation":[{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China"},{"name":"School of Artificial Intelligence, Nanjing University of Information Science & Technology, Nanjing 210044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9932-0914","authenticated-orcid":false,"given":"Chunbiao","family":"Li","sequence":"additional","affiliation":[{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China"},{"name":"School of Artificial Intelligence, Nanjing University of Information Science & Technology, Nanjing 210044, China"}]},{"given":"Haibo","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China"}]},{"given":"Yibo","family":"Zhao","sequence":"additional","affiliation":[{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China"}]},{"given":"Yanling","family":"Wang","sequence":"additional","affiliation":[{"name":"Collaborative Innovation Center of Memristive Computing Application (CICMCA), Qilu Institute of Technology, Jinan 250200, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"143904","DOI":"10.1103\/PhysRevLett.91.143904","article-title":"Optical multistability in three-level atoms inside an optical ring cavity","volume":"91","author":"Joshi","year":"2003","journal-title":"Phys. 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