{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:32:16Z","timestamp":1773815536768,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,10]],"date-time":"2021-06-10T00:00:00Z","timestamp":1623283200000},"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"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>An absolute value function was introduced for chaos construction, where hyperchaotic oscillation was found with amplitude rescaling. The nonlinear absolute term brings the convenience for amplitude control. Two regimes of amplitude control including total and partial amplitude control are discussed, where the attractor can be rescaled separately by two independent coefficients. Symmetrical pairs of coexisting attractors are captured by corresponding initial conditions. Circuit implementation by the platform STM32 is consistent with the numerical exploration and the theoretical observation. This finding is helpful for promoting discrete map application, where amplitude control is realized in an easy way and coexisting symmetrical sequences with opposite polarity are obtained.<\/jats:p>","DOI":"10.3390\/sym13061047","type":"journal-article","created":{"date-parts":[[2021,6,10]],"date-time":"2021-06-10T03:48:08Z","timestamp":1623296888000},"page":"1047","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A 2D Hyperchaotic Map: Amplitude Control, Coexisting Symmetrical Attractors and Circuit Implementation"],"prefix":"10.3390","volume":"13","author":[{"given":"Xuejiao","family":"Zhou","sequence":"first","affiliation":[{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), 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"},{"name":"Collaborative Innovation Center of Memristive Computing Application (CICMCA), Qilu Institute of Technology, Jinan 250200, China"}]},{"given":"Xu","family":"Lu","sequence":"additional","affiliation":[{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5243-1046","authenticated-orcid":false,"given":"Tengfei","family":"Lei","sequence":"additional","affiliation":[{"name":"Collaborative Innovation Center of Memristive Computing Application (CICMCA), Qilu Institute of Technology, Jinan 250200, 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"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"107373","DOI":"10.1016\/j.sigpro.2019.107373","article-title":"Characteristic analysis of the fractional-order hyperchaotic complex system and its image encryption application","volume":"169","author":"Yang","year":"2020","journal-title":"Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1607","DOI":"10.1007\/s11071-017-3752-2","article-title":"Multistability analysis, circuit implementations and application in image encryption of a novel memristive chaotic circuit","volume":"90","author":"Peng","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Deng, J., Zhou, M., Wang, C., Wang, S., and Xu, C. 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