Dynamical Analysis of Two Cell Cycles with Delay Feedback Control

Dynamical Analysis of Two Cell Cycles with Delay Feedback Control | 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Research Article Dynamical Analysis of Two Cell Cycles with Delay Feedback Control Suqi Ma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2633189/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 Double Hopf bifurcation of codimension 2 singularity in a type of two cells oscillator with interaction feedback connection is investigated. With the introduction of time delay which represents the communication time between cells, the stability switching phenomena is observed and double Hopf bifurcation occurs at the intersection point of Hopf lines. The geometrical scheme is applied in analyzing system stability underlying multiple time delays. The numerical simulation discovers that either the vicinity of bifurcating periodical solution on the margin of Hopf lines or the coexistence phenomena of five periodical solutions induced by stability switching phenomena. By applying the Schmidt dimensional reduction technique combined with the center manifold theory, the normal form of double Hopf point is calculated by parameter perturbation method and the near dynamics of double Hopf point is classified. The bifurcating periodical solutions and quasi-periodical solutions are observed which are in consistence with the numerical simulation results. 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-2633189","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":179332610,"identity":"a32e6d5b-1fb7-4a4c-ac50-79f8227174b9","order_by":0,"name":"Suqi Ma","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwUlEQVRIiWNgGAWjYDADNvbGxocfSNPCc7jZWII0ayTS2wR4iFHI337GdMOPP4dl+yQftjFIMNjJ6TYQMvtMjtnN3rbDxm3SiW0PChiSjc0OENBiwJBjdoO34XAiUEu7gQTDgcRtBLXwvzG7+ecPUIvkwTYJHqK0SOSY3eZhA2qRYCRSi8SNZ2W3ZdvSjdt4EoGBbECEX/j7k7fdfPPHWnZ++/GHDz9U2MkR1AIDjA0QdxKpHEnLKBgFo2AUjAIsAABRFEOcfvawTAAAAABJRU5ErkJggg==","orcid":"","institution":"China Agricultural University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Suqi","middleName":"","lastName":"Ma","suffix":""}],"badges":[],"createdAt":"2023-02-27 09:29:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2633189/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2633189/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":35104732,"identity":"f46865dc-7306-4058-86a6-f2aace7e76a4","added_by":"auto","created_at":"2023-03-31 14:29:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1158883,"visible":true,"origin":"","legend":"","description":"","filename":"ddmaa.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2633189/v1_covered.pdf"},{"id":33639675,"identity":"42f7499e-ea87-4795-9154-3a140a94e58f","added_by":"auto","created_at":"2023-03-01 17:15:24","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1150316,"visible":true,"origin":"","legend":"","description":"","filename":"ddmaa.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2633189/v1/f27e6550fca3467de2a61a33.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eDynamical Analysis of Two Cell Cycles with Delay Feedback Control\u003c/p\u003e","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-2633189/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2633189/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Double Hopf bifurcation of codimension 2 singularity in a type of two cells oscillator with interaction feedback connection is investigated. 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