Optimal Control of Reaction-Diffusion Vegetation Models with Multiple Human Intervention Strategies

Optimal Control of Reaction-Diffusion Vegetation Models with Multiple Human Intervention Strategies | 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 Optimal Control of Reaction-Diffusion Vegetation Models with Multiple Human Intervention Strategies Huimin Wang, Huimin Bai, Jianchao Zeng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9304258/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 11 You are reading this latest preprint version Abstract Vegetation patterns are important indicators of ecosystem health and stability, and their formation and evolution are influenced by multiple factors, among which human intervention plays a key role. However, existing studies that integrate human interventions with optimal control theory for the regulation of vegetation patterns remain limited, and most focus on the case of a single control variable, thereby making it difficult to capture the synergistic effects of multiple intervention measures. To address this issue, this paper constructs an optimal control model for vegetation-water dynamics with two control variables under reaction-diffusion framework. The two controls represent human interventions such as fertilization or trampling, and vegetation introduction or land clearing, respectively, and an objective functional is formulated to balance ecological benefits and control costs. Through numerical simulations, three control strategies formed by different combinations of the two control variables are systematically compared and analyzed. The results show that all strategies can effectively regulate vegetation patterns, among which the coordinated action of the two control variables achieves the most cost-effectiveness. Further analysis reveals that excessively large cost weights weaken the control effect and lead to increases in both relative control error and the objective functional value. In contrast, the terminal weights exert a relatively limited influence on vegetation increment, whereas the average control intensity and relative error are more sensitive to variations in the vegetation terminal weight. The study reveals the regulatory mechanisms of human interventions on vegetation pattern evolution, and characterizes the trade-off between control costs and ecological benefits, which provides a theoretical basis and decision-making reference for ecological restoration and sustainable ecosystem management. Cost-effectiveness Human intervention Vegetation pattern transformation Reaction-diffusion model Optimal control Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 11 May, 2026 Reviews received at journal 11 May, 2026 Reviewers agreed at journal 03 May, 2026 Reviews received at journal 29 Apr, 2026 Reviewers agreed at journal 29 Apr, 2026 Reviewers agreed at journal 06 Apr, 2026 Reviewers agreed at journal 06 Apr, 2026 Reviewers invited by journal 03 Apr, 2026 Editor assigned by journal 03 Apr, 2026 Submission checks completed at journal 03 Apr, 2026 First submitted to journal 02 Apr, 2026 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-9304258","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":619724983,"identity":"40912dd3-4d32-4505-86d0-ac5d3066c350","order_by":0,"name":"Huimin Wang","email":"","orcid":"","institution":"Taiyuan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Huimin","middleName":"","lastName":"Wang","suffix":""},{"id":619724984,"identity":"8ae06a74-cbd2-415a-804f-5472cc584a17","order_by":1,"name":"Huimin Bai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVRIiWNgGAWjYBACAwbGNhDJw8DeABZgbCBeC88BorUwsEFYEglEajFnP9z2mKdgm4y55NtjEj8YbGQ3HGB+9gCfFsuexHZjHoPbPJaz89IkexjSjDccYDM3wOuwA4lt0iAtBrdzzKQZGA4nbjjAwyaBV8v5h1AtN8+AtPwnQssNmC03eEBaDhDWYjnjYZvkHJCWMznGlj0GycYzD7OZ4dVizp/+TOLNn9v2BsfPGN74UWEn23e8+RleLejuBGJmEtSPglEwCkbBKMAOAATSRGFmmnIZAAAAAElFTkSuQmCC","orcid":"","institution":"North University of China","correspondingAuthor":true,"prefix":"","firstName":"Huimin","middleName":"","lastName":"Bai","suffix":""},{"id":619724985,"identity":"ddac5b3b-0bc1-4dc6-b03a-40c248d46e06","order_by":2,"name":"Jianchao Zeng","email":"","orcid":"","institution":"North University of China","correspondingAuthor":false,"prefix":"","firstName":"Jianchao","middleName":"","lastName":"Zeng","suffix":""}],"badges":[],"createdAt":"2026-04-02 14:13:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9304258/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9304258/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106482690,"identity":"e48489a5-138c-414a-9066-c4b5000bfcc3","added_by":"auto","created_at":"2026-04-09 05:20:04","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":14791006,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9304258/v1_covered_0fd650e8-c096-435a-aa9b-126c7a080d75.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Optimal Control of Reaction-Diffusion Vegetation Models with Multiple Human Intervention Strategies","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Cost-effectiveness, Human intervention, Vegetation pattern transformation, Reaction-diffusion model, Optimal control","lastPublishedDoi":"10.21203/rs.3.rs-9304258/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9304258/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Vegetation patterns are important indicators of ecosystem health and stability, and their formation and evolution are influenced by multiple factors, among which human intervention plays a key role. 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