Construction Algorithm of Non-degenerate Complex Domain Chaotic System with Application on PRNG

Construction Algorithm of Non-degenerate Complex Domain Chaotic System with Application on PRNG | 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 Construction Algorithm of Non-degenerate Complex Domain Chaotic System with Application on PRNG Xu Dai, Xiaotong Wang, Haotong Han, Erfu Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4418005/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 12 Sep, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted 13 You are reading this latest preprint version Abstract Based on the theory of eigenvalue estimation, this paper proposes a construction algorithm for N-dimensional discrete non-degenerate chaotic system defined in complex domain. Through theoretical analysis, it's proved that the system constructed by the algorithm not only exhibits non-degenerate properties in complex domain, but also maintains non-degeneracy for its real and imaginary components. In order to verify the effectiveness and feasibility, the example of a three-dimensional discrete complex domain chaotic system is taken. The dynamic properties of this system is thoroughly analyzed including the chaotic generation mechanism, Lyapunov exponents (LEs), chaotic phase diagram and sequence statistical characteristics. The algorithm reversely manages the positional relationship between the Gerschgorin disk of the coefficient matrix and the unit circle, ensuring all eigenvalues fall within the desired range. Subsequently, a non-degenerate chaotic system is constructed in which all LEs are positive. Finally, the algorithm is applied to a Pseudo-Random Number Generator (PRNG), and various indicators are experimentally analyzed. The results demonstrate that the constructed PRNG exhibits favorable statistical characteristics and is excellent for application in secure communication. Gerschgorin disk theorem PRNG Non-degeneracy Complex domain chaos Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 12 Sep, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 11 Jul, 2024 Reviews received at journal 14 Jun, 2024 Reviews received at journal 10 Jun, 2024 Reviewers agreed at journal 05 Jun, 2024 Reviews received at journal 03 Jun, 2024 Reviewers agreed at journal 03 Jun, 2024 Reviewers agreed at journal 03 Jun, 2024 Reviewers agreed at journal 03 Jun, 2024 Reviewers agreed at journal 02 Jun, 2024 Reviewers invited by journal 02 Jun, 2024 Editor assigned by journal 27 May, 2024 Submission checks completed at journal 20 May, 2024 First submitted to journal 14 May, 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. 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-4418005","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":307327786,"identity":"86618b68-48c0-431c-ac90-839c7cabbf8b","order_by":0,"name":"Xu Dai","email":"","orcid":"","institution":"Heilongjiang University","correspondingAuthor":false,"prefix":"","firstName":"Xu","middleName":"","lastName":"Dai","suffix":""},{"id":307327787,"identity":"b3f2abe5-f5fa-4dc3-8f81-fffbef173eb9","order_by":1,"name":"Xiaotong Wang","email":"","orcid":"","institution":"Heilongjiang University","correspondingAuthor":false,"prefix":"","firstName":"Xiaotong","middleName":"","lastName":"Wang","suffix":""},{"id":307327788,"identity":"68e40d4b-15b0-4a9a-a233-fa65d139f8f2","order_by":2,"name":"Haotong Han","email":"","orcid":"","institution":"Heilongjiang University","correspondingAuthor":false,"prefix":"","firstName":"Haotong","middleName":"","lastName":"Han","suffix":""},{"id":307327789,"identity":"4d12bc68-e208-4db3-bcfd-ad74ccde15b9","order_by":3,"name":"Erfu Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYPACOQZ+CeYGAyCLsYFILcYMkjMYSdVicAOimLAWg+NnD7/4uMcgcfPtxoZiHgYb2Q0HmJ89wKvlTF6a5YxnBonb7hxsMOZhSDPecIDN3ACfFrMDOWbGPAf+JG67kQjScjhxwwEeNgm8Ws6/MTP+cwDosBlgLf+J0HIjx/gxA1DLBgmwlgOEtdjfeGPG2HPAwHgG0GGGcwySjWceZjPDq0WyP8f4w48DBrL9M5KPGbypsJPtO978DK8WIIA7g82AARRUzATUg5R8gDEeEFY8CkbBKBgFIxEAAGT6TtUjtIuEAAAAAElFTkSuQmCC","orcid":"","institution":"Heilongjiang University","correspondingAuthor":true,"prefix":"","firstName":"Erfu","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2024-05-14 09:21:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4418005/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4418005/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-024-10167-z","type":"published","date":"2024-09-12T15:57:28+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":64619070,"identity":"0b5295e8-9b84-4b43-8d6c-1965e27852bb","added_by":"auto","created_at":"2024-09-16 16:11:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1643557,"visible":true,"origin":"","legend":"","description":"","filename":"ConstructionAlgorithmofNondegenerateComplexDomainChaoticSystemwithApplicationonPRNG.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4418005/v1_covered_d2bbf1f7-101e-4034-a9b8-75d9556fce6c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Construction Algorithm of Non-degenerate Complex Domain Chaotic System with Application on PRNG","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":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Gerschgorin disk theorem, PRNG, Non-degeneracy, Complex domain chaos","lastPublishedDoi":"10.21203/rs.3.rs-4418005/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4418005/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Based on the theory of eigenvalue estimation, this paper proposes a construction algorithm for N-dimensional discrete non-degenerate chaotic system defined in complex domain. Through theoretical analysis, it's proved that the system constructed by the algorithm not only exhibits non-degenerate properties in complex domain, but also maintains non-degeneracy for its real and imaginary components. In order to verify the effectiveness and feasibility, the example of a three-dimensional discrete complex domain chaotic system is taken. The dynamic properties of this system is thoroughly analyzed including the chaotic generation mechanism, Lyapunov exponents (LEs), chaotic phase diagram and sequence statistical characteristics. The algorithm reversely manages the positional relationship between the Gerschgorin disk of the coefficient matrix and the unit circle, ensuring all eigenvalues fall within the desired range. Subsequently, a non-degenerate chaotic system is constructed in which all LEs are positive. Finally, the algorithm is applied to a Pseudo-Random Number Generator (PRNG), and various indicators are experimentally analyzed. The results demonstrate that the constructed PRNG exhibits favorable statistical characteristics and is excellent for application in secure communication.","manuscriptTitle":"Construction Algorithm of Non-degenerate Complex Domain Chaotic System with Application on PRNG","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-31 02:26:05","doi":"10.21203/rs.3.rs-4418005/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-07-11T12:42:13+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-14T10:30:13+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-10T14:16:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"185995971453525452497377475481460269443","date":"2024-06-05T23:52:43+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-03T16:03:27+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"129110134288506260259110303454804944102","date":"2024-06-03T08:10:12+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"90348278165336982387849538370482439656","date":"2024-06-03T06:54:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"188445729134377482793591450179475567890","date":"2024-06-03T06:10:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"106185782737757254678675446546455104065","date":"2024-06-03T00:28:46+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-06-02T22:07:18+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-05-27T15:00:15+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-05-20T22:25:06+00:00","index":"","fulltext":""},{"type":"submitted","content":"Nonlinear Dynamics","date":"2024-05-14T09:18:37+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"6aea2b35-a1a9-44eb-be76-a55175358c46","owner":[],"postedDate":"May 31st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-09-16T16:01:44+00:00","versionOfRecord":{"articleIdentity":"rs-4418005","link":"https://doi.org/10.1007/s11071-024-10167-z","journal":{"identity":"nonlinear-dynamics","isVorOnly":false,"title":"Nonlinear Dynamics"},"publishedOn":"2024-09-12 15:57:28","publishedOnDateReadable":"September 12th, 2024"},"versionCreatedAt":"2024-05-31 02:26:05","video":"","vorDoi":"10.1007/s11071-024-10167-z","vorDoiUrl":"https://doi.org/10.1007/s11071-024-10167-z","workflowStages":[]},"version":"v1","identity":"rs-4418005","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4418005","identity":"rs-4418005","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}