Chaotic System with Zero Dissipation Measure on Centered Sphere

Chaotic System with Zero Dissipation Measure on Centered Sphere | 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PDF Article Chaotic System with Zero Dissipation Measure on Centered Sphere Jiri Petrzela This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7357056/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 Autonomous third-order chaotic dynamical system with zero dissipation measure on centered sphere is discussed in this paper. Radius of this sphere represents one of system´s parameters. Starting from cyclically symmetrical vector field, algebraically the simplest form of mathematical description is obtained (at least so far, based on thorough literature review). Generated strange attractor is interestingly shaped, with significant degree of entropy, randomness, and long-term unpredictability. In frame of numerical investigation, dynamical behavior is quantified using concept of Lyapunov exponents, spectral and approximate entropy. To prove robustness of generated chaotic attractor, continuous-time system integration is demonstrated via flow-equivalent lumped electronic circuit design, construction, and experimental verification. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations No competing interests reported. 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7357056","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":512130101,"identity":"127d7839-c4c5-4a77-8b0a-38087e8fe4ee","order_by":0,"name":"Jiri Petrzela","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4UlEQVRIiWNgGAWjYBACxmYGhgMw9gGGCiAlQaQWsLoDDGeI0AIDEC2MbURoYW7nfXiAcYdNnXn/4QMHfs47nMcv3cD48Qdeh7EbHGA8kyYhc+BYwsHebYeLJeccYJbAZxNjMxvIPYclJBh7DA7wbjucuOFGAhuDAWEt/yUkmPk/HPw7B6olgbCWAxISbDwMh3kboFoOENKSeCZZcgYPm8FhmWPpiTPnHGyWbMCjxbD/GPOHjzvs+CX4Dz98+KbGOrFfuvkg3hAzBJmXiGooIz47GBjkiVAzCkbBKBgFIx0AAARMT8VXqN/uAAAAAElFTkSuQmCC","orcid":"","institution":"University of Defence","correspondingAuthor":true,"prefix":"","firstName":"Jiri","middleName":"","lastName":"Petrzela","suffix":""}],"badges":[],"createdAt":"2025-08-12 14:53:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7357056/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7357056/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106976009,"identity":"9880e897-0619-4a53-9e9b-cdf7f545e384","added_by":"auto","created_at":"2026-04-15 10:43:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3351739,"visible":true,"origin":"","legend":"","description":"","filename":"paper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7357056/v1_covered_7cd19059-75c3-4355-974c-7f926187c6b5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Chaotic System with Zero Dissipation Measure on Centered Sphere","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"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},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7357056/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7357056/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAutonomous third-order chaotic dynamical system with zero dissipation measure on centered sphere is discussed in this paper. 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