System design and dynamic analysis of a new type of controllable multi-scroll chaotic system and its application in multi-image encryption

System design and dynamic analysis of a new type of controllable multi-scroll chaotic system and its application in multi-image encryption | 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 System design and dynamic analysis of a new type of controllable multi-scroll chaotic system and its application in multi-image encryption Jie Fang, Nian Guo, Jiabin Wang, Junyao Hu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6671953/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Dec, 2025 Read the published version in International Journal of Dynamics and Control → Version 1 posted You are reading this latest preprint version Abstract In this paper, a new type of controllable and switchable multi-scroll chaotic system family is proposed and designed based on sign function and system switching. The mathematical model of the multi-scroll chaotic system includes switchable function terms and the switchable function includes summation section of sign function. The phase diagram and equilibrium point of the multi-scroll chaotic system are theoretically analyzed and numerically simulated, which indicate that the controllable and switchable multi-scroll chaotic system can exhibit more complex topological structures and dynamic behaviors. By selecting different switching function and system parameters, the system can present honeycomb-shaped or twist-shaped multi-scroll chaotic attractors in phase plane. The number of generated scrolls can be controlled by adjusting the upper bound of the summation function. The 4×3 switchable multi-scroll chaotic system is chosen as a example to analyze the chaotic dynamic behavior, such as Lyapunov exponent spectrum, bifurcation diagram, maximum Lyapunov exponent. The corresponding analog circuit of the 4×3 multi-scroll chaotic system is designed to verify the correctness and feasibility of the proposed system. Finally, the designed multi-scroll chaotic system is combined with the improved Hilbert curve and dynamic RNA diffusion for multi-image encryption. The proposed approach demonstrates excellent encryption performance. Chaotic system Multi-scroll Switching function Dynamic behavior Analog circuit Multi-image encryption Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 27 Dec, 2025 Read the published version in International Journal of Dynamics and Control → 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. 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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-6671953","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":459596745,"identity":"b4687520-cfe7-482e-8dd9-103a7a16af17","order_by":0,"name":"Jie Fang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYBAC9gYgkfhHgoexmYHxQUKFDWEtPAeAxMcGCxmgFmaDB2fSiNPCOLMBbDqb5MO2Q0RoYT97+DXvDgke5nbmYxUJbAcY+Nu7E/Br4clLs+Y9A/ILW9qNBJ47DBJnzm7Aq8WeIcfMmIcNpIXH7EaCxDMGA4lc/Fp4+N/AtPB/K0gwOEyEFokc44cz28C2sDEkJBCl5Y0ZwweIX4wlEg6k8RD0Cw9/jvGHhIo6e8P+ww8//vxnI8ff3otfCxCwSYBIwwaoGYSUgwDzBxApT4zSUTAKRsEoGJkAAOsVRTbv85BuAAAAAElFTkSuQmCC","orcid":"","institution":"Shanghai Maritime University","correspondingAuthor":true,"prefix":"","firstName":"Jie","middleName":"","lastName":"Fang","suffix":""},{"id":459596746,"identity":"99249cda-3d53-4272-9e2e-969172e848a1","order_by":1,"name":"Nian Guo","email":"","orcid":"","institution":"Shanghai Maritime University","correspondingAuthor":false,"prefix":"","firstName":"Nian","middleName":"","lastName":"Guo","suffix":""},{"id":459596747,"identity":"2a301707-3624-4f51-a899-d9a0f6870e19","order_by":2,"name":"Jiabin Wang","email":"","orcid":"","institution":"Zhengzhou University of Light Industry","correspondingAuthor":false,"prefix":"","firstName":"Jiabin","middleName":"","lastName":"Wang","suffix":""},{"id":459596749,"identity":"b6986e3e-1c1d-46c9-8643-95ec6ea349b0","order_by":3,"name":"Junyao Hu","email":"","orcid":"","institution":"Shanghai Maritime University","correspondingAuthor":false,"prefix":"","firstName":"Junyao","middleName":"","lastName":"Hu","suffix":""}],"badges":[],"createdAt":"2025-05-15 11:08:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6671953/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6671953/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40435-025-01961-7","type":"published","date":"2025-12-27T15:57:07+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":99172237,"identity":"ef488ac9-9712-41ee-b1c3-df605348b3f6","added_by":"auto","created_at":"2025-12-29 16:04:49","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7562920,"visible":true,"origin":"","legend":"","description":"","filename":"MANUSCRIPT.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6671953/v1_covered_b0cdb75c-9ebe-4d68-a879-91c7bf525428.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"System design and dynamic analysis of a new type of controllable multi-scroll chaotic system and its application in multi-image encryption","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"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":"Chaotic system, Multi-scroll, Switching function, Dynamic behavior, Analog circuit, Multi-image encryption","lastPublishedDoi":"10.21203/rs.3.rs-6671953/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6671953/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, a new type of controllable and switchable multi-scroll chaotic system family is proposed and designed based on sign function and system switching. The mathematical model of the multi-scroll chaotic system includes switchable function terms and the switchable function includes summation section of sign function. The phase diagram and equilibrium point of the multi-scroll chaotic system are theoretically analyzed and numerically simulated, which indicate that the controllable and switchable multi-scroll chaotic system can exhibit more complex topological structures and dynamic behaviors. By selecting different switching function and system parameters, the system can present honeycomb-shaped or twist-shaped multi-scroll chaotic attractors in phase plane. The number of generated scrolls can be controlled by adjusting the upper bound of the summation function. The 4\u0026times;3 switchable multi-scroll chaotic system is chosen as a example to analyze the chaotic dynamic behavior, such as Lyapunov exponent spectrum, bifurcation diagram, maximum Lyapunov exponent. The corresponding analog circuit of the 4\u0026times;3 multi-scroll chaotic system is designed to verify the correctness and feasibility of the proposed system. Finally, the designed multi-scroll chaotic system is combined with the improved Hilbert curve and dynamic RNA diffusion for multi-image encryption. 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