Dynamical Behaviour and Applications of Master-slave Fractional-order Non-volatile Memristor Chaotic Hopfield Neural Network

Dynamical Behaviour and Applications of Master-slave Fractional-order Non-volatile Memristor Chaotic Hopfield Neural Network | 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 Dynamical Behaviour and Applications of Master-slave Fractional-order Non-volatile Memristor Chaotic Hopfield Neural Network Binshuai Feng, Zeyu Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5934729/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 May, 2025 Read the published version in Nonlinear Dynamics → Version 1 posted 10 You are reading this latest preprint version Abstract In this work, a discrete fractional-order memristor is proposed and proven to be non-volatile, which can be used to model synaptic connections between neurons. Based on the proposed memristor, we put forward a novel fractional order non-volatile memristor chaotic Hopfield neural network, utilizing a time-scale-based difference method for decoupling. The dynamical behaviours of the suggested fractional-order system are analyzed through phase diagram, Lyapunov exponent, divergence, stability analysis of equilibrium point and bifurcation diagram. A master-slave system is constructed based on the proposed system, thereby achieving synchronization and a novel image encryption approach is proposed, grounded in the master-slave hyperchaotic system obtained. The experimental findings indicate that the encrypted image exhibits an approximately uniform pixel distribution and adjacent pixel correlations close to zero, making it robust to statistical analysis attacks. Furthermore, the algorithm demonstrates resilience to differential attack, information entropy analysis and chosen plaintext attack. As a consequence of the parameter sensitivity of the proposed hyperchaotic system, the proposed encryption scheme features a considerable key space. Chaotic dynamics Discrete fractional calculus Hopfield neural network Image encryption Memristor Synchronization Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 23 May, 2025 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 10 Apr, 2025 Reviews received at journal 10 Apr, 2025 Reviewers agreed at journal 31 Mar, 2025 Reviews received at journal 21 Feb, 2025 Reviewers agreed at journal 11 Feb, 2025 Reviewers agreed at journal 10 Feb, 2025 Reviewers invited by journal 07 Feb, 2025 Editor assigned by journal 07 Feb, 2025 Submission checks completed at journal 31 Jan, 2025 First submitted to journal 31 Jan, 2025 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-5934729","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":409577489,"identity":"815fbbfd-840f-41f5-8c80-e405f5531f9c","order_by":0,"name":"Binshuai Feng","email":"","orcid":"","institution":"Northwest A\u0026F University","correspondingAuthor":false,"prefix":"","firstName":"Binshuai","middleName":"","lastName":"Feng","suffix":""},{"id":409577490,"identity":"11be2ff7-0a16-4833-9238-b501c21f221f","order_by":1,"name":"Zeyu Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4UlEQVRIiWNgGAWjYBACPmYILQehbID4AAEtbFAtxhAqjRgtUDqxgXgt7DzGHz62HU7fLpH+TOJHAoMc340Exs8FeB3GY2A4s+1w7s4ZOWaSPQkMxpI3EpilZxDQkswL1LLhdg6bBO8PhsQNNxKAggS0HP4LdJjB7fRnkn8SGOqJ0WLYzNh2OMHgdoKZNE8CQ4IBYS1sxYw959INN9x/Y2wtkyBhOPPMw2ZpfFr4+Q9v/vCjzFre4MzxhzffJNjI8x1PPvgZnxYwYGSDMyVA3AZCGoDgDxFqRsEoGAWjYOQCAEMXRjNs0jwMAAAAAElFTkSuQmCC","orcid":"","institution":"Northwest A\u0026F University","correspondingAuthor":true,"prefix":"","firstName":"Zeyu","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2025-01-31 08:23:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5934729/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5934729/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-025-11306-w","type":"published","date":"2025-05-23T15:57:47+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":83460672,"identity":"9dc5c991-5cb8-4ce9-a3c7-0a07ed3c6fb6","added_by":"auto","created_at":"2025-05-26 16:13:29","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":23198439,"visible":true,"origin":"","legend":"","description":"","filename":"snarticletemplate.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5934729/v1_covered_5f60b053-4029-4dac-b087-8bd012fc3dd6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dynamical Behaviour and Applications of Master-slave Fractional-order Non-volatile Memristor Chaotic Hopfield Neural Network","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":"Chaotic dynamics, Discrete fractional calculus, Hopfield neural network, Image encryption, Memristor, Synchronization","lastPublishedDoi":"10.21203/rs.3.rs-5934729/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5934729/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this work, a discrete fractional-order memristor is proposed and proven to be non-volatile, which can be used to model synaptic connections between neurons. 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