Global Stability Analysis of a Predator–Prey Model Incorporating Prey Cannibalism and Intraspecific Competition

Global Stability Analysis of a Predator–Prey Model Incorporating Prey Cannibalism and Intraspecific Competition | 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 Global Stability Analysis of a Predator–Prey Model Incorporating Prey Cannibalism and Intraspecific Competition Ahmed Buseri Ashine This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8630134/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 This study extends the local stability analysis of a predator-prey model with prey cannibalism and interspecific competition among predators[1]. We investigate the global stability of the coexistence equilibrium E* and the predator-free equilibrium E N ​. Using a conducted Lyapunov function and Dulac’s criterion, we prove that under certain parametric conditions, E* is globally asymptotically stable in the interior of the first quadrant. Numerical simulations confirm the analytical results and illustrate the basin of attraction. This work provide a more complete understanding of the long term dynamics of ecological system with cannibalistic and competitive interactions. Global stability Lypunov function predator-prey model cannibalism intraspecific competition 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. 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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-8630134","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":591174280,"identity":"2d95ca40-1775-4f4c-8884-d570a2d231f0","order_by":0,"name":"Ahmed Buseri Ashine","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABD0lEQVRIiWNgGAWjYDACCSDmbQCxGBsfAEkesCgPkVqaDVC04NSG0MLAJgEXxaeFf3Z34oO3Ow7b80sfbqv4uadOxuB2A+ODt20Mcva4LLlzdrPh3DOHE2f2Jbbd7Hl2mMfgzgFmw7ltDMY4HXYjd5s0b9vhBIMzjG03eA4c4DG4kcAGFGFI7MGhQ/5G7vbfQC329kAthX8O1IG0sANFGOpxaTEA2sIM1MK4gYexjZnnADPYFqAIQwIuhxneyN0sOfdMeuKMM4zN0jIHDvNI3khslpxzTsKw5wB2LXI3cjd+eLvD2p6/h/3hxzcH6uz5biQf/PCmzEaevQGX/zEBI0itBCFVo2AUjIJRMArwAABRFlyGqHBhkQAAAABJRU5ErkJggg==","orcid":"","institution":"Arsi University","correspondingAuthor":true,"prefix":"","firstName":"Ahmed","middleName":"Buseri","lastName":"Ashine","suffix":""}],"badges":[],"createdAt":"2026-01-18 08:53:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8630134/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8630134/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105273135,"identity":"fdd75d9c-6787-4cda-8f72-5d394b755da6","added_by":"auto","created_at":"2026-03-24 08:59:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":518034,"visible":true,"origin":"","legend":"","description":"","filename":"GlobalStabilityAnalysisofaPredatorPreyModelIncorporatingPreyCannibalismandIntraspecificCompetition.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8630134/v1_covered_b23e9b66-b8ef-4eb7-bc30-afe5358ea774.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Global Stability Analysis of a Predator–Prey Model Incorporating Prey Cannibalism and Intraspecific Competition","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":"Global stability, Lypunov function, predator-prey model, cannibalism, intraspecific competition","lastPublishedDoi":"10.21203/rs.3.rs-8630134/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8630134/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study extends the local stability analysis of a predator-prey model with prey cannibalism and interspecific competition among predators[1]. We investigate the global stability of the coexistence equilibrium \u003cem\u003e\u003cstrong\u003eE*\u003c/strong\u003e\u003c/em\u003e and the predator-free equilibrium \u003cem\u003e\u003cstrong\u003eE\u003c/strong\u003e\u003c/em\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003eN\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e​. Using a conducted Lyapunov function and Dulac’s criterion, we prove that under certain parametric conditions, \u003cem\u003e\u003cstrong\u003eE*\u003c/strong\u003e\u003c/em\u003e is globally asymptotically stable in the interior of the first quadrant. Numerical simulations confirm the analytical results and illustrate the basin of attraction. 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