Functional and numerical analysis by ensuring positivity methods for Leslie-Gower-Bazykin prey-predator models

Functional and numerical analysis by ensuring positivity methods for Leslie-Gower-Bazykin prey-predator models | 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 Functional and numerical analysis by ensuring positivity methods for Leslie-Gower-Bazykin prey-predator models Shun Kondo, Michinori Kouno, Okihiro Sawada This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7202555/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 Time-global unique nonnegative classical solutions to the reaction-diffusion equations of the Leslie-Gower prey-predator models with the Bazykin fractional response are constructed. The crucial step is to prove the existence of time-local nonnegative classical solutions, using new successive approximation associated with time evolution operators by ensuring positivity method of approximation sequences. Numerical analysis is also discussed with the same spirits by ensuring positivity method. reaction diffusion equation prey-predator model time evolution operator ensuring positivity method 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. 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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-7202555","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":502631998,"identity":"55fd5abb-c226-44ea-a462-b8d2af5f6c46","order_by":0,"name":"Shun Kondo","email":"","orcid":"","institution":"Kitami Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Shun","middleName":"","lastName":"Kondo","suffix":""},{"id":502631999,"identity":"770339dd-43e9-4c02-b86d-d32f5252a08d","order_by":1,"name":"Michinori Kouno","email":"data:image/png;base64,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","orcid":"","institution":"Kitami Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Michinori","middleName":"","lastName":"Kouno","suffix":""},{"id":502632000,"identity":"81c04753-b8c8-48f3-a6fa-47b83906d8c4","order_by":2,"name":"Okihiro Sawada","email":"","orcid":"","institution":"Kitami Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Okihiro","middleName":"","lastName":"Sawada","suffix":""}],"badges":[],"createdAt":"2025-07-24 07:23:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7202555/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7202555/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90083407,"identity":"d4d9d8b0-fa99-47c5-9a55-c00f237e473a","added_by":"auto","created_at":"2025-08-28 09:25:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":282914,"visible":true,"origin":"","legend":"","description":"","filename":"PP2KKS20250717.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7202555/v1_covered_3144c978-52e5-4419-ae67-dfe62045e2ea.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Functional and numerical analysis by ensuring positivity methods for Leslie-Gower-Bazykin prey-predator models","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":"reaction diffusion equation, prey-predator model, time evolution operator, ensuring positivity method","lastPublishedDoi":"10.21203/rs.3.rs-7202555/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7202555/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Time-global unique nonnegative classical solutions to the reaction-diffusion equations of the Leslie-Gower prey-predator models with the Bazykin fractional response are constructed. 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