Dynamic analysis of a novel 3D chaotic map with two internal frequencies

Dynamic analysis of a novel 3D chaotic map with two internal frequencies | 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 Dynamic analysis of a novel 3D chaotic map with two internal frequencies Pei Wang, Qiao Wang, Haiwei Sang, Kunshuai Li, Xiong Yu, WeiCheng Xiong This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5267914/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 18 Feb, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract Trigonometric functions serving as boundary functions are excellent nonlinear elements in designing chaotic maps. However, research on the dynamical behaviors dependent on the internal frequency within these boundary functions is not yet sufficient. Hence, in this paper, a novel chaotic map is proposed. Numerical simulations reveal the unique dynamical behaviors dependent on its dominant and recessive internal frequencies, including the control of the map's Lyapunov exponents and their impact on the overall system performance. this unique phenomenon has not been reported before. The system's initial-boosting behavior is then captured, further revealing its super-extreme multistability. This map is implemented on STM32 platform, demonstrating its practical applicability for potential practical application scenarios. Ultimately, The map is applied in designing a pseudo-random number generator, and its high randomness is validated through NIST SP800-22 test. Chaotic map Internal frequency Lyapunov exponent Offset boosting Super Extreme multistability Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 18 Feb, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 10 Dec, 2024 Reviews received at journal 01 Dec, 2024 Reviews received at journal 01 Dec, 2024 Reviewers agreed at journal 21 Nov, 2024 Reviewers agreed at journal 21 Nov, 2024 Reviewers invited by journal 21 Nov, 2024 Editor assigned by journal 10 Nov, 2024 Editor invited by journal 08 Nov, 2024 Submission checks completed at journal 07 Nov, 2024 First submitted to journal 15 Oct, 2024 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. 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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-5267914","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":381030752,"identity":"10d7794b-2aff-49c5-b4b3-387d297de383","order_by":0,"name":"Pei Wang","email":"","orcid":"","institution":"Guizhou Education University","correspondingAuthor":false,"prefix":"","firstName":"Pei","middleName":"","lastName":"Wang","suffix":""},{"id":381030753,"identity":"a7dc8863-fc37-42d7-b8a1-e6b57837286c","order_by":1,"name":"Qiao Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVRIiWNgGAWjYNACAwYGfiiTsYFoLZINpGkB6TpArBaD42cPv3hTYCdnfH75swc/GGxkNxxgfvYAr5YzeWmWcwySjc1uPEg37GFIM95wgM3cAJ8WswM5ZsY8BsyJ224cOCbNwHA4ccMBHjYJvFrOvwFpqU/cPONgG1DLfyK03MgxfsxjADScv5kNqOUAYS32N96YMc4xOG4scYONTbIH6KmZh9nM8GqR7M8x/vDmT7Ucf//xZxI/Kuxk+443P8OrBQjYJHhAlEQCAzhOGZgJqAcp+QDWwn+AsNJRMApGwSgYmQAAwIpJiCbduoYAAAAASUVORK5CYII=","orcid":"","institution":"Guizhou Education University","correspondingAuthor":true,"prefix":"","firstName":"Qiao","middleName":"","lastName":"Wang","suffix":""},{"id":381030754,"identity":"7adcf366-a94c-4b00-96cc-0dfe5f240db4","order_by":2,"name":"Haiwei Sang","email":"","orcid":"","institution":"Guizhou Education University","correspondingAuthor":false,"prefix":"","firstName":"Haiwei","middleName":"","lastName":"Sang","suffix":""},{"id":381030755,"identity":"853796b8-797d-41bb-b3e9-63828b02d346","order_by":3,"name":"Kunshuai Li","email":"","orcid":"","institution":"Guizhou University","correspondingAuthor":false,"prefix":"","firstName":"Kunshuai","middleName":"","lastName":"Li","suffix":""},{"id":381030756,"identity":"c796c95e-61df-4fd5-ae42-a63eeb54e92c","order_by":4,"name":"Xiong Yu","email":"","orcid":"","institution":"Universiti Kebangsaan Malaysia","correspondingAuthor":false,"prefix":"","firstName":"Xiong","middleName":"","lastName":"Yu","suffix":""},{"id":381030757,"identity":"43589738-4ad2-4662-aad5-e898e3ad6d80","order_by":5,"name":"WeiCheng Xiong","email":"","orcid":"","institution":"Guizhou Education University","correspondingAuthor":false,"prefix":"","firstName":"WeiCheng","middleName":"","lastName":"Xiong","suffix":""}],"badges":[],"createdAt":"2024-10-15 10:23:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5267914/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5267914/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-90596-x","type":"published","date":"2025-02-18T15:58:04+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":77052700,"identity":"019fd18e-1835-41a8-8ea4-1c16d270c9e7","added_by":"auto","created_at":"2025-02-24 16:23:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2051589,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5267914/v1_covered_184bd1f6-dec8-448e-9a8b-104cb2969d81.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dynamic analysis of a novel 3D chaotic map with two internal frequencies","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Chaotic map, Internal frequency, Lyapunov exponent, Offset boosting, Super Extreme multistability","lastPublishedDoi":"10.21203/rs.3.rs-5267914/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5267914/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTrigonometric functions serving as boundary functions are excellent nonlinear elements in designing chaotic maps. 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