The simplest 4-D autonomous hyperchaotic system coined: Theoretical analysis and analog circuit design

The simplest 4-D autonomous hyperchaotic system coined: Theoretical analysis and analog circuit design | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The simplest 4-D autonomous hyperchaotic system coined: Theoretical analysis and analog circuit design Yongyong Xiong, Xiao Zhang, Jean Chamberlain Chedjou, Yesen Wu, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4843584/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this paper, a new fourth-order autonomous hyperjerk system capable of producing hyperchaotic signals (FHHO hereafter) is proposed. The proposed model features a single nonlinear term represented by the hyperbolic sine of the weighted sum of two state variables (i.e., the fundamental variable and the jerk). The FHHO system is dissipative and symmetric and has a single unstable equilibrium point located at the origin of the state space. To describe the mechanisms leading to chaos and subsequent hyperchaos, a systematic study is carried out using appropriate analysis tools, such as Lyapunov exponent graphs, phase portraits, Poincaré maps, and bifurcation diagrams. We highlight rich and varied dynamics marked by periodic, tori, chaotic or hyperchaotic attractors and, even more interestingly, offset control and symmetry control properties. The electronic simulator of the proposed FHHO model is built using only five operational amplifiers (i.e., four integrators and a summing amplifier) and a pair of diodes mounted head to tail. The experimental results confirm the presence of hyperchaotic signals as well as the bifurcation modes predicted by the theoretical study. To the best of our knowledge, the hyperchaotic model studied combines the two forms of simplicity rarely encountered, namely, the simplicity of the evolution equations and the simplicity of electronic realization. Simplest hyperchaotic system Lyapunov exponents Poincaré sections offset and symmetry controls analog electronic simulator Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4843584","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":335259840,"identity":"ee29467c-da6f-4b30-8ffc-b5d202363d96","order_by":0,"name":"Yongyong Xiong","email":"","orcid":"","institution":"Jingdezhen Vocational University of Art, Jingdezhen 333000, China.","correspondingAuthor":false,"prefix":"","firstName":"Yongyong","middleName":"","lastName":"Xiong","suffix":""},{"id":335259841,"identity":"889d56b8-b81d-4816-9e34-c64edc6821be","order_by":1,"name":"Xiao Zhang","email":"","orcid":"","institution":"Gongqing Institute of Science and Technology, Jiujiang 332020, China.","correspondingAuthor":false,"prefix":"","firstName":"Xiao","middleName":"","lastName":"Zhang","suffix":""},{"id":335259842,"identity":"6f134227-f266-4328-902d-881596b34091","order_by":2,"name":"Jean Chamberlain Chedjou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4klEQVRIiWNgGAWjYBACxgYwdQCIgPgDyVoYZ4A5zERZdgCMmHmI0cLc3vzsAUPNHTm+g4ePSdvU2CU2sJ8/gN9hPcfMDRiOPTOWPHAsTTrnWHJiA08yflsYZySYSTA2HE7ccOCMmXQOG3NiAwMhLfOffwNpqQdrsfhXn9jA/5iQLTxgWxIMQFoY2w4nNkgQsqUnp0wi4dhhw5kHjiVb9vYdN26TeGyAV4th+/FtEh9qDsvz3Th88MaPb9Wy/fyJD/BraQASCSCWxAGICBt+ZzEwyMNZ/A2E1I6CUTAKRsFIBQDixU1S4slAnwAAAABJRU5ErkJggg==","orcid":"","institution":"Transportation informatics group (TIG), University of Klagenfurt, 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The proposed model features a single nonlinear term represented by the hyperbolic sine of the weighted sum of two state variables (i.e., the fundamental variable and the jerk). The FHHO system is dissipative and symmetric and has a single unstable equilibrium point located at the origin of the state space. To describe the mechanisms leading to chaos and subsequent hyperchaos, a systematic study is carried out using appropriate analysis tools, such as Lyapunov exponent graphs, phase portraits, Poincar\u0026eacute; maps, and bifurcation diagrams. We highlight rich and varied dynamics marked by periodic, tori, chaotic or hyperchaotic attractors and, even more interestingly, offset control and symmetry control properties. The electronic simulator of the proposed FHHO model is built using only five operational amplifiers (i.e., four integrators and a summing amplifier) and a pair of diodes mounted head to tail. The experimental results confirm the presence of hyperchaotic signals as well as the bifurcation modes predicted by the theoretical study. To the best of our knowledge, the hyperchaotic model studied combines the two forms of simplicity rarely encountered, namely, the simplicity of the evolution equations and the simplicity of electronic realization.\u003c/p\u003e","manuscriptTitle":"The simplest 4-D autonomous hyperchaotic system coined: Theoretical analysis and analog circuit design","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-06 00:10:55","doi":"10.21203/rs.3.rs-4843584/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"cea95eac-27e1-4d78-8bae-5ea4ac5cdc29","owner":[],"postedDate":"August 6th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-08-06T00:10:55+00:00","versionOfRecord":[],"versionCreatedAt":"2024-08-06 00:10:55","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4843584","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4843584","identity":"rs-4843584","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}