{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T00:11:10Z","timestamp":1773447070372,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,4]],"date-time":"2020-04-04T00:00:00Z","timestamp":1585958400000},"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\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51974045"],"award-info":[{"award-number":["51974045"]}],"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>By introducing a simple feedback, a hyperchaotic hidden attractor is found in the newly proposed Lorenz-like chaotic system. Some variables of the equilibria-free system can be controlled in amplitude and offset by an independent knob. A circuit experiment based on Multisim is consistent with the theoretic analysis and numerical simulation.<\/jats:p>","DOI":"10.3390\/sym12040550","type":"journal-article","created":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T03:40:19Z","timestamp":1586403619000},"page":"550","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["A Symmetric Controllable Hyperchaotic Hidden Attractor"],"prefix":"10.3390","volume":"12","author":[{"given":"Xin","family":"Zhang","sequence":"first","affiliation":[{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science &amp; Technology, Nanjing 210044, China"},{"name":"Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science &amp; Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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 &amp; Technology, Nanjing 210044, China"},{"name":"Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science &amp; Technology, Nanjing 210044, China"},{"name":"Collaborative Innovation Center of Memristive Computing Application (CICMCA), Qilu Institute of Technology, Jinan 250200, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zuohua","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changyuan","family":"Tao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1007\/s11071-013-0866-z","article-title":"Amplitude control approach for chaotic signals","volume":"73","author":"Li","year":"2013","journal-title":"Nonlinear Dyn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2059","DOI":"10.1007\/s11071-014-1568-x","article-title":"Finding coexisting attractors using amplitude control","volume":"78","author":"Li","year":"2014","journal-title":"Nonlinear Dyn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1007\/s11071-018-4162-9","article-title":"A flexible chaotic system with adjustable amplitude, largest Lyapunov exponent, and local Kaplan\u2013Yorke dimension and its usage in engineering applications","volume":"92","author":"Chen","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"033114","DOI":"10.1063\/1.4979039","article-title":"Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N + 1-scroll chaotic attractors system","volume":"27","author":"Wang","year":"2017","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1750158","DOI":"10.1142\/S0218126617501584","article-title":"A switchable chaotic oscillator with two amplitude-frequency controllers","volume":"26","author":"Hu","year":"2017","journal-title":"J. Circuits Syst. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"083101","DOI":"10.1063\/1.4997051","article-title":"A new chaotic oscillator with free control","volume":"27","author":"Li","year":"2017","journal-title":"Chaos"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1530025","DOI":"10.1142\/S0218127415300256","article-title":"Constructing chaotic systems with total amplitude control","volume":"25","author":"Li","year":"2015","journal-title":"Int. J. Bifurc. 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D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2577","DOI":"10.1007\/s11071-017-3396-2","article-title":"Memristive oscillator based on Chua\u2019s circuit: stability analysis and hidden dynamics","volume":"88","author":"Rocha","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1049\/el.2016.0563","article-title":"Extreme multistability in a memristive circuit","volume":"52","author":"Bao","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.chaos.2017.12.023","article-title":"Coexisting attractors and circuit implementation of a new 4D chaotic system with two equilibria","volume":"107","author":"Lai","year":"2018","journal-title":"Chaos Solitons Fractals"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3113","DOI":"10.7498\/aps.56.3113","article-title":"A hyperchaotic Lorenz attractor and its circuit implementation","volume":"56","author":"Wang","year":"2007","journal-title":"Acta Phys. Sin."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.chaos.2013.08.018","article-title":"Simple chaotic flows with a line equilibrium","volume":"57","author":"Jafari","year":"2013","journal-title":"Chaos Solitons Fractals"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.cnsns.2017.10.001","article-title":"Initial condition dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria","volume":"57","author":"Bao","year":"2018","journal-title":"Commun. Nonlinear Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1650098","DOI":"10.1142\/S021812741650098X","article-title":"A simple chaotic flow with a plane of equilibria","volume":"26","author":"Jafari","year":"2016","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_19","first-page":"699","article-title":"Elementary quadratic chaotic flows with no equilibria","volume":"377","author":"Jafari","year":"2013","journal-title":"Phys. Lett. Sect. A Gen. Atomic Solid State Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.chaos.2016.11.016","article-title":"Hidden extreme multistability in memristive hyperchaotic system","volume":"94","author":"Bao","year":"2017","journal-title":"Chaos Solitons Fractals"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.chaos.2017.12.017","article-title":"A hidden chaotic attractor in the classical lorenz system","volume":"107","author":"Munmuangsaen","year":"2018","journal-title":"Chaos Solitons Fractals"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3000","DOI":"10.1016\/j.ijleo.2015.12.089","article-title":"Research on a new 3d autonomous chaotic system with coexisting attractors","volume":"127","author":"Lai","year":"2016","journal-title":"Optik\u2014Int. J. Light Electron Opt."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s11071-015-2144-8","article-title":"Study of hidden attractors, multiple limit cycles from hopf bifurcation and boundedness of motion in the generalized hyperchaotic rabinovich system","volume":"82","author":"Wang","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1002\/cta.2339","article-title":"A novel no-equilibrium hyperchaotic multi-wing system via introducing memristor","volume":"46","author":"Zhou","year":"2018","journal-title":"Int. J. Circ. Theor. App."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1007\/s11071-011-0284-z","article-title":"A hyperchaotic system without equilibrium","volume":"69","author":"Wang","year":"2012","journal-title":"Nonlinear Dyn."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1016\/j.chaos.2005.08.019","article-title":"Chaotic hyperjerk systems","volume":"28","author":"Chlouverakis","year":"2006","journal-title":"Chaos Solitons Fractals"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"073107","DOI":"10.1063\/1.4958296","article-title":"Extreme multistability in a memristor- based multi-scroll hyperchaotic system","volume":"26","author":"Yuan","year":"2016","journal-title":"Chaos"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"190502","DOI":"10.7498\/aps.65.190502","article-title":"Memristor-based Lorenz hyper-chaotic system and its circuit implementation","volume":"65","author":"Ruan","year":"2016","journal-title":"Acta Phys. Sin."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1650177","DOI":"10.1142\/S0218127413501526","article-title":"Generation of multi-wing chaotic attractors from a lorenz-like system","volume":"23","author":"Lai","year":"2013","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"010509","DOI":"10.1088\/1674-1056\/20\/1\/010509","article-title":"A new four dimensional hyperchaotic Lorenz system and its adaptive control","volume":"20","author":"Si","year":"2011","journal-title":"Chin. Phys. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"030509","DOI":"10.1088\/1674-1056\/19\/3\/030509","article-title":"Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation","volume":"19","author":"Wang","year":"2010","journal-title":"Chin. Phys. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1750027","DOI":"10.1142\/S0218127417500274","article-title":"Generating Four-Wing Hyperchaotic Attractor and Two-Wing, Three-Wing, and Four-Wing Chaotic Attractors in 4D Memristive System","volume":"27","author":"Zhou","year":"2017","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"368986","DOI":"10.1155\/2014\/368986","article-title":"A memristive hyperchaotic system without equilibrium","volume":"2014","author":"Pham","year":"2014","journal-title":"Sci. World J."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"159194","DOI":"10.1155\/2013\/159194","article-title":"Dual synchronization of fractional-order chaotic systems via a linear controller","volume":"2013","author":"Xiao","year":"2013","journal-title":"Sci. World J."},{"key":"ref_35","first-page":"490364","article-title":"One adaptive synchronization approach for fractional-order chaotic system with fractional-order","volume":"2","author":"Zhou","year":"2014","journal-title":"Sci. World J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1950117","DOI":"10.1142\/S0218127419501177","article-title":"Multiscroll hyperchaotic system with hidden attractors and its circuit implementation","volume":"29","author":"Zhang","year":"2019","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"013113","DOI":"10.1063\/1.5006214","article-title":"Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability","volume":"28","author":"Zhang","year":"2018","journal-title":"Chaos"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2424","DOI":"10.1016\/j.ijleo.2015.11.099","article-title":"Simplified hyper-chaotic systems generating multi-wing non-equilibrium attractor","volume":"127","author":"Wang","year":"2016","journal-title":"Optik"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s11071-013-1101-7","article-title":"Analytical and numerical investigation of a new lorenz-like chaotic attractor with compound structures","volume":"75","author":"Cang","year":"2014","journal-title":"Nonlinear Dyn."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1334","DOI":"10.1007\/s11071-017-3729-1","article-title":"Diagnosing multistability by offset boosting","volume":"90","author":"Li","year":"2017","journal-title":"Nonlinear Dyn."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/4\/550\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:15:24Z","timestamp":1760174124000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/4\/550"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,4]]},"references-count":40,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["sym12040550"],"URL":"https:\/\/doi.org\/10.3390\/sym12040550","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,4]]}}}