Global Dynamics and Time-Optimal Control Studies for Additional Food provided Holling Type-III Mutually Interfering Prey-Predator Systems with Applications to Pest Management

Global Dynamics and Time-Optimal Control Studies for Additional Food provided Holling Type-III Mutually Interfering Prey-Predator Systems with Applications to Pest Management | 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 Dynamics and Time-Optimal Control Studies for Additional Food provided Holling Type-III Mutually Interfering Prey-Predator Systems with Applications to Pest Management D Bhanu Prakash, D K K Vamsi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5254784/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract In this study, we derive and study an additional food provided prey-predator model involving Holling type-III functional response among mutually interfering predators. This study investigates the effects of provision of additional food to natural enemies (predators) in altering pest (prey) dynamics. The preliminary results include positivity and boundedness of the solutions. We demonstrate the existence of equilibria, their local stability and bifurcation analysis. We also discuss the global dynamics and stability behavior with respect to crucial parameters using numerical methods. Our results show that the additional food influence the system dynamics and controlled provision of additional food is beneficial for pest management. Further, time optimal control problems are explored by considering the quality and quantity of additional food as control parameters. We framed and characterized the time optimal control problems using Pontryagin’s maximum principle and simulated using numerical optimization techniques. Our theoretical and numerical investigations reveal that the provision of suitable choice of additional food steers the system to a prey-elimination state, leading to a pest-regulated ecosystems. Our work uniquely integrates mutual interference among predators and slow predation dynamics with the provision of additional food, coupled with time optimal control strategies, offering a novel perspective on sustainable pest management and bio-control. MSC 2020 codes: 37A50; 60H10; 60J65; 60J70 Prey - Predator Model Holling type-III Response Mutual Interference Additional Food Global Dynamics Time Optimal Control Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 28 Apr, 2025 Reviews received at journal 15 Apr, 2025 Reviewers agreed at journal 01 Apr, 2025 Reviewers agreed at journal 01 Apr, 2025 Editor assigned by journal 31 Mar, 2025 Reviewers invited by journal 18 Mar, 2025 Submission checks completed at journal 17 Mar, 2025 First submitted to journal 08 Mar, 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. 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-5254784","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":447970522,"identity":"45f4fe8a-18ce-4019-a35a-28230844950b","order_by":0,"name":"D Bhanu Prakash","email":"","orcid":"","institution":"Sri Sathya Sai Institute of Higher Learning","correspondingAuthor":false,"prefix":"","firstName":"D","middleName":"Bhanu","lastName":"Prakash","suffix":""},{"id":447970523,"identity":"a2f0b74f-3484-450e-9e69-1d0776f92bb2","order_by":1,"name":"D K K Vamsi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVRIie3PsarCMBSA4SOCLtGuJ6A+w5GCOAi+ikFw6uATFOFCXLz4LC7BsSLUJeLqWgpOCjp2EEwDTldb3e6Qn3AyfSQHwOX6j+mavZiXTzHrmzmyp5zwmSX4OQGKzKg8SVFNHU8wC8KWf9il12SN4NUDgmT9nvC9jPmv2rLeMeih0Ah8cSYQ+j2hQ/2HGioyhNVASAQ6mleELCbduwqZvzQfy8mwlOzlJm2oKiMYEdpXsIRwHYu0bXZBu4tEhvo0jYpIU09oc1Hh0DMfu2Vy0PHm41WSFZA/sXxEXwCXy+VyvegB9JRS2PTjShAAAAAASUVORK5CYII=","orcid":"","institution":"Sri Sathya Sai Institute of Higher Learning","correspondingAuthor":true,"prefix":"","firstName":"D","middleName":"K K","lastName":"Vamsi","suffix":""}],"badges":[],"createdAt":"2024-10-13 10:08:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5254784/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5254784/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81521466,"identity":"b570211f-5f11-47b7-b6d4-b66b68f30d85","added_by":"auto","created_at":"2025-04-28 08:07:05","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5216006,"visible":true,"origin":"","legend":"","description":"","filename":"RevisedManuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5254784/v1_covered_c4534401-4409-401e-ba69-325170797c10.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Global Dynamics and Time-Optimal Control Studies for Additional Food provided Holling Type-III Mutually Interfering Prey-Predator Systems with Applications to Pest Management","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":"discover-applied-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Applied Sciences](https://link.springer.com/journal/42452)","snPcode":"42452","submissionUrl":"https://submission.springernature.com/new-submission/42452/3","title":"Discover Applied Sciences","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Prey - Predator Model, Holling type-III Response, Mutual Interference, Additional Food, Global Dynamics, Time Optimal Control","lastPublishedDoi":"10.21203/rs.3.rs-5254784/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5254784/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, we derive and study an additional food provided prey-predator model involving Holling type-III functional response among mutually interfering predators. This study investigates the effects of provision of additional food to natural enemies (predators) in altering pest (prey) dynamics. The preliminary results include positivity and boundedness of the solutions. We demonstrate the existence of equilibria, their local stability and bifurcation analysis. We also discuss the global dynamics and stability behavior with respect to crucial parameters using numerical methods. Our results show that the additional food influence the system dynamics and controlled provision of additional food is beneficial for pest management. Further, time optimal control problems are explored by considering the quality and quantity of additional food as control parameters. We framed and characterized the time optimal control problems using Pontryagin’s maximum principle and simulated using numerical optimization techniques. 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