{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T23:56:35Z","timestamp":1789775795131,"version":"4.0.1"},"reference-count":40,"publisher":"AIP Publishing","issue":"3","funder":[{"name":"South African National Research Foundation Incentive Grant","award":["114911"],"award-info":[{"award-number":["114911"]}]},{"name":"South Afican Eskom Tertiary Education Support Programme"},{"DOI":"10.13039\/501100012659","name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61873186"],"award-info":[{"award-number":["61873186"]}],"id":[{"id":"10.13039\/501100012659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"South African National Research Foundation","award":["112142 and 112108"],"award-info":[{"award-number":["112142 and 112108"]}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2020,3,1]]},"abstract":"<jats:p>This paper reports a generic method for constructing n-fold covers of 3D conservative chaotic systems, which is derived from the theory of the generalized Hamiltonian system. Three typical example systems are constructed based on the proposed method, and their different n-fold cover chaotic flows are investigated theoretically and numerically. For each example system, the motion trajectories are both conservative and chaotic, which can be verified by the Lyapunov exponents, and it is interesting to find that the emergence of n-fold cover conservative chaos mainly relays on the corresponding Hamiltonian. Numerical results show that the proposed generic method is effective to construct n-fold covers of 3D conservative chaotic systems, such as a 3-fold cover in the direction of the y-axis, 2\u00d73-fold cover on the x\u2013y plane, and 2\u00d73\u00d72-fold cover in the 3D phase space. This study also demonstrates that based on appropriate skew-symmetric nonconstant matrices, the n-fold cover conservative chaos can be obtained by changing the Hamiltonian.<\/jats:p>","DOI":"10.1063\/1.5123246","type":"journal-article","created":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T08:36:26Z","timestamp":1583138186000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":34,"title":["A generic method for constructing\n                    <i>n<\/i>\n                    -fold covers of 3D conservative chaotic systems"],"prefix":"10.1063","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7168-9640","authenticated-orcid":false,"given":"Shijian","family":"Cang","sequence":"first","affiliation":[{"name":"Department of Product Design, Tianjin University of Science and Technology 1 , Tianjin 300457, China"},{"name":"College of Electronic Information and Automation, Tianjin University of Science and Technology 2 , Tianjin 300222, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electronic Information and Automation, Tianjin University of Science and Technology 2 , Tianjin 300222, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhijun","family":"Kang","sequence":"additional","affiliation":[{"name":"College of Electronic Information and Automation, Tianjin University of Science and Technology 2 , Tianjin 300222, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3025-336X","authenticated-orcid":false,"given":"Zenghui","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Electrical and Mining Engineering, University of South Africa 3 , Florida 1710, South Africa"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2020,3,2]]},"reference":[{"key":"2023070318335839300_c1","volume-title":"A First Course in Chaotic Dynamical Systems: Theory and Experiment","year":"2018"},{"key":"2023070318335839300_c2","doi-asserted-by":"publisher","first-page":"024102","DOI":"10.1103\/PhysRevLett.120.024102","article-title":"Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach","volume":"120","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"2023070318335839300_c3","doi-asserted-by":"publisher","first-page":"939","DOI":"10.1007\/s11071-017-3920-4","article-title":"New class of chaotic systems with equilibrium points like a three-leaved clover","volume":"91","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"2023070318335839300_c4","doi-asserted-by":"publisher","first-page":"2879","DOI":"10.1007\/s11071-018-4531-4","article-title":"Autonomous memristor chaotic systems of infinite chaotic attractors and circuitry realization","volume":"94","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"2023070318335839300_c5","volume-title":"Regular and Chaotic Oscillations","year":"2001"},{"key":"2023070318335839300_c6","volume-title":"Introduction to Applied Nonlinear Dynamical Systems and Chaos","year":"2003"},{"key":"2023070318335839300_c7","doi-asserted-by":"publisher","first-page":"2429","DOI":"10.1109\/LPT.2015.2466092","article-title":"Chaos-based partial transmit sequence technique for physical layer security in OFDM-PON","volume":"27","year":"2015","journal-title":"IEEE Photonics Technol. Lett."},{"key":"2023070318335839300_c8","doi-asserted-by":"publisher","first-page":"2137","DOI":"10.1109\/TIFS.2018.2812080","article-title":"Depreciating motivation and empirical security analysis of chaos-based image and video encryption","volume":"13","year":"2018","journal-title":"IEEE Trans. Inf. Forensics Security"},{"key":"2023070318335839300_c9","doi-asserted-by":"publisher","first-page":"1850114","DOI":"10.1142\/S0218127418501146","article-title":"Cryptanalysis of chaos-based cryptosystem from the hardware perspective","volume":"28","year":"2018","journal-title":"Int. J. Bifurcat. Chaos"},{"key":"2023070318335839300_c10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jksuci.2018.05.012","article-title":"Level by level image compression-encryption algorithm based on quantum chaos map","year":"2018","journal-title":"J. King Saud Univ. Comput. Inf. Sci."},{"key":"2023070318335839300_c11","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1103\/RevModPhys.53.643","article-title":"Roads to turbulence in dissipative dynamical systems","volume":"53","year":"1981","journal-title":"Rev. Mod. Phys."},{"key":"2023070318335839300_c12","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/s11071-018-4056-x","article-title":"Brief review on application of nonlinear dynamics in image encryption","volume":"92","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"2023070318335839300_c13"},{"key":"2023070318335839300_c14","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/S0167-2789(97)82008-8","article-title":"Extraction of delay information from chaotic time series based on information entropy","volume":"108","year":"1997","journal-title":"Physica D"},{"key":"2023070318335839300_c15"},{"key":"2023070318335839300_c16"},{"key":"2023070318335839300_c17","doi-asserted-by":"publisher","first-page":"3056","DOI":"10.1016\/j.cnsns.2008.11.005","article-title":"A new substitution\u2013diffusion based image cipher using chaotic standard and logistic maps","volume":"14","year":"2009","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"2023070318335839300_c18","doi-asserted-by":"publisher","first-page":"240503","DOI":"10.7498\/aps.61.240503","article-title":"Grid multi-scroll chaotic attractors in hybrid image encryption algorithm based on current conveyor","volume":"61","year":"2012","journal-title":"Acta Phys. Sin."},{"key":"2023070318335839300_c19"},{"key":"2023070318335839300_c20","doi-asserted-by":"publisher","first-page":"4350","DOI":"10.1016\/j.amc.2010.11.009","article-title":"Automatic synthesis of chaotic attractors","volume":"217","year":"2011","journal-title":"Appl. Math. Comput."},{"key":"2023070318335839300_c21","doi-asserted-by":"publisher","first-page":"016206","DOI":"10.1103\/PhysRevE.63.016206","article-title":"Covering dynamical systems: Twofold covers","volume":"63","year":"2000","journal-title":"Phys. Rev. E"},{"key":"2023070318335839300_c22","doi-asserted-by":"publisher","first-page":"036220","DOI":"10.1103\/PhysRevE.66.036220","article-title":"Multichannel intermittencies induced by symmetries","volume":"66","year":"2002","journal-title":"Phys. Rev. E"},{"key":"2023070318335839300_c23","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/0375-9601(93)90735-I","article-title":"The proto-Lorenz system","volume":"178","year":"1993","journal-title":"Phys. Lett. A"},{"key":"2023070318335839300_c24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1142\/S0218127405011990","article-title":"A gallery of attractors from smooth Chua\u2019s equation","volume":"15","year":"2005","journal-title":"Int. J. Bifurcat. Chaos"},{"key":"2023070318335839300_c25","volume-title":"The Topology of Chaos: Alice in Stretch and Squeezeland","year":"2012"},{"key":"2023070318335839300_c26","volume-title":"Topology and Dynamics of Chaos: In Celebration of Robert Gilmore\u2019s 70th Birthday","year":"2013"},{"key":"2023070318335839300_c27","doi-asserted-by":"publisher","first-page":"067202","DOI":"10.1103\/PhysRevE.64.067202","article-title":"Unimodal order in the image of the simplest equivariant chaotic system","volume":"64","year":"2001","journal-title":"Phys. Rev. E"},{"key":"2023070318335839300_c28","doi-asserted-by":"publisher","first-page":"R647","DOI":"10.1103\/PhysRevE.50.R647","article-title":"Some simple chaotic flows","volume":"50","year":"1994","journal-title":"Phys. Rev. E"},{"key":"2023070318335839300_c29","doi-asserted-by":"publisher","first-page":"1850087","DOI":"10.1142\/S0218127418500876","article-title":"Conservative chaos in a class of nonconservative systems: Theoretical analysis and numerical demonstrations","volume":"28","year":"2018","journal-title":"Int. J. Bifurcat. Chaos"},{"key":"2023070318335839300_c30","doi-asserted-by":"publisher","first-page":"1830044","DOI":"10.1142\/S0218127418300446","article-title":"Single crystal-lattice-shaped chaotic and quasi-periodic flows with time-reversible symmetry","volume":"28","year":"2018","journal-title":"Int. J. Bifurcat. Chaos"},{"key":"2023070318335839300_c31","doi-asserted-by":"publisher","first-page":"1950021","DOI":"10.1142\/S0218127419500214","article-title":"Categories of conservative flows","volume":"29","year":"2019","journal-title":"Int. J. Bifurcat. Chaos"},{"key":"2023070318335839300_c32","doi-asserted-by":"publisher","first-page":"91","DOI":"10.11499\/sicejl1962.39.91","article-title":"Port-controlled Hamiltonian systems: Towards a theory for control and design of nonlinear physical systems","volume":"39","year":"2000","journal-title":"J. Soc. Instrum. Control Eng."},{"key":"2023070318335839300_c33","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1561\/2600000002","article-title":"Port-Hamiltonian systems theory: An introductory overview","volume":"1","year":"2014","journal-title":"Foundations Trends Syst. Control"},{"key":"2023070318335839300_c34","doi-asserted-by":"publisher","first-page":"101102","DOI":"10.1063\/1.5054850","article-title":"Qualitative stability and synchronicity analysis of power network models in port-Hamiltonian form","volume":"28","year":"2017","journal-title":"Chaos"},{"key":"2023070318335839300_c35","doi-asserted-by":"publisher","first-page":"073113","DOI":"10.1063\/1.5087876","article-title":"A chaos to chaos control approach for controlling the chaotic dynamical systems using Hamilton energy feedback and fuzzy-logic system","volume":"29","year":"2019","journal-title":"Chaos"},{"key":"2023070318335839300_c36","doi-asserted-by":"publisher","first-page":"1750024","DOI":"10.1142\/S0218127417500249","article-title":"Distinguishing Lorenz and Chen systems based upon Hamiltonian energy theory","volume":"27","year":"2017","journal-title":"Int. J. Bifurcat. Chaos"},{"key":"2023070318335839300_c37","doi-asserted-by":"publisher","first-page":"759","DOI":"10.1103\/PhysRevE.51.759","article-title":"Remark on \u201cSome simple chaotic flows\u201d","volume":"51","year":"1995","journal-title":"Phys. Rev. E"},{"key":"2023070318335839300_c38","doi-asserted-by":"publisher","first-page":"123110","DOI":"10.1063\/1.4937167","article-title":"A vast amount of various invariant tori in the Nos\u00e9-Hoover oscillator","volume":"25","year":"2015","journal-title":"Chaos"},{"key":"2023070318335839300_c39","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.1007\/s11071-018-4125-1","article-title":"On the existence of periodic orbits and KAM tori in the Sprott A system: A special case of the Nos\u00e9\u2013Hoover oscillator","volume":"92","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"2023070318335839300_c40","doi-asserted-by":"publisher","first-page":"1730005","DOI":"10.1142\/S0218127417300051","article-title":"Dynamics of Hamiltonian systems and memristor circuits","volume":"27","year":"2017","journal-title":"Int. J. Bifurcat. Chaos"}],"container-title":["Chaos: An Interdisciplinary Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/1.5123246\/14623292\/033103_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/1.5123246\/14623292\/033103_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T17:54:02Z","timestamp":1688406842000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/cha\/article\/30\/3\/033103\/342228\/A-generic-method-for-constructing-n-fold-covers-of"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,1]]},"references-count":40,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,3,1]]}},"URL":"https:\/\/doi.org\/10.1063\/1.5123246","relation":{},"ISSN":["1054-1500","1089-7682"],"issn-type":[{"value":"1054-1500","type":"print"},{"value":"1089-7682","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,3]]},"published":{"date-parts":[[2020,3,1]]},"article-number":"033103"}}