Propagation and blocking of bistable waves by variable diffusion

Propagation and blocking of bistable waves by variable diffusion | 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 Propagation and blocking of bistable waves by variable diffusion Hirokazu Ninomiya, Keita Nakajima This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5457898/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 Biological diffusion processes are often influenced by environmental factors. In this study, we investigate the effects of variable diffusion, which depend on the point between the departure and the arrival points, on the propagation of bistable waves. This process includes neutral, repulsive, and attractive transitions. Using singular limit analysis, we derive the equation for the interface between two stable states and examine the relationship between wave propagation and variable diffusion. In particular, when the transition probability depends on the environment at the dividing point between the departure and the arrival points, we derived an expression for the wave propagation speed that includes this dividing point ratio. More specifically, the threshold between wave propagation and conditional blocking in a one-dimensional space occurs when the transition probability is determined by a dividing point ratio of 3:1 between the departure and the arrival points. Furthermore, as an application of this concept, we consider the Aliev-Panfilov model to explore the mechanism for generating spiral patterns. Mathematical and Theoretical Biology Applied Mathematics reaction-diffusion equations propagation variable diffusion singular limit problem transition probability Full Text Additional Declarations The authors declare no competing interests. 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. 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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-5457898","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":378602583,"identity":"e6fb1951-d53d-4ea3-afea-b6e5badf5583","order_by":0,"name":"Hirokazu Ninomiya","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDElEQVRIiWNgGAWjYBACA2YGBsYGMBNMSTAwsINoAwtStPAcAIlL4NbCANcCAxIJDBC9OIA5O+/DhzNq6hIbpJvbHnzMsUjsn/n86oYfBRIM/O3dCdi0WDazGxtuOMaW2CBzsN1w5jaJxBm3c8pu9gAdJnHm7AasDjvMxib5gI0nsUEisU2aF6il4XZO2g0eoBYDiVw8Wv5JILTMv3km7eYfQlo2thkgtGy4wX7sNgFbmA1n9iUYtwG1SAL9YrzxTA7bbRkDCR6cfjl/jPFhz7c62X6J9GcSH7fVyc47fvzZzTd/bOT423uxaoEDNijt2MDAA4osBh68ypGBPTDFPCBa9SgYBaNgFIwIAACbg2JCmwHqqwAAAABJRU5ErkJggg==","orcid":"","institution":"Meiji University","correspondingAuthor":true,"prefix":"","firstName":"Hirokazu","middleName":"","lastName":"Ninomiya","suffix":""},{"id":378602584,"identity":"37d67f05-523d-427c-9668-f9d80d180eee","order_by":1,"name":"Keita Nakajima","email":"","orcid":"","institution":"Meiji University","correspondingAuthor":false,"prefix":"","firstName":"Keita","middleName":"","lastName":"Nakajima","suffix":""}],"badges":[],"createdAt":"2024-11-15 05:56:05","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-5457898/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5457898/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":69200017,"identity":"c0d866d1-3a7e-40b5-aba6-7b127052c08f","added_by":"auto","created_at":"2024-11-18 02:34:14","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1567820,"visible":true,"origin":"","legend":"","description":"","filename":"NakajimaNinomiyasubmitfinalpreprint.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5457898/v1_covered_ff8518fc-ef96-4c3e-bc78-5300f6366c98.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003ePropagation and blocking of bistable waves by variable diffusion\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"reaction-diffusion equations, propagation, variable diffusion, singular limit problem, transition probability","lastPublishedDoi":"10.21203/rs.3.rs-5457898/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5457898/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBiological diffusion processes are often influenced by environmental factors. 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