Dynamic equilibrium, stability and sensitivity analysis of anthropogenic metal cycles with an application to copper

Dynamic equilibrium, stability and sensitivity analysis of anthropogenic metal cycles with an application to copper | 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 Dynamic equilibrium, stability and sensitivity analysis of anthropogenic metal cycles with an application to copper Nicola Gambaro, Pablo Brito-Parada, Yves Plancherel This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9199322/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 Anthropogenic metal cycles shape resource availability, recycling performance and long-term sustainability: understanding their dynamic behaviour, including long-term stability and sensitivity to change, is essential for sustainable resource management and supply-chain resilience. Here, a system of ordinary differential equations for the global copper cycle linking extraction, processing, manufacturing, use, waste management and recycling is developed to analyse the dynamic equilibrium, stability and sensitivity of metal cycles. Results demonstrate that dissipative losses are necessary for asymptotic stability of the stocks, underscoring the importance of quantifying dissipation and recycling for long-term forecasting. Multi-decadal copper inventory oscillations can be simulated by integrating a second-order investment accelerator to endogenise mining dynamics, while also creating conditions for endogenous growth. Sensitivity analysis shows that new and old scrap rates exert the largest influence on the system's dynamics, whereas refining and manufacturing flows provide the strongest stabilising effect. This study extends material flow analysis with tools from dynamical systems theory by linking physical flows with economic feedbacks and offers a general framework for assessing stability, resilience and policy levers in metal cycles and other resource systems. anthropogenic metal cycles dynamical systems stability analysis copper material flow analysis sensitivity analysis 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-9199322","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":621371397,"identity":"d9aba0a7-3889-490d-b3d1-5bea9bb1e125","order_by":0,"name":"Nicola Gambaro","email":"data:image/png;base64,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","orcid":"","institution":"Imperial College London","correspondingAuthor":true,"prefix":"","firstName":"Nicola","middleName":"","lastName":"Gambaro","suffix":""},{"id":621371398,"identity":"6df717aa-44eb-4cf2-8a66-8953a8e11cae","order_by":1,"name":"Pablo Brito-Parada","email":"","orcid":"","institution":"Imperial College London","correspondingAuthor":false,"prefix":"","firstName":"Pablo","middleName":"","lastName":"Brito-Parada","suffix":""},{"id":621371399,"identity":"a5a4a21c-2cd1-4650-b851-7c8b73c1a0c4","order_by":2,"name":"Yves Plancherel","email":"","orcid":"","institution":"Imperial College London","correspondingAuthor":false,"prefix":"","firstName":"Yves","middleName":"","lastName":"Plancherel","suffix":""}],"badges":[],"createdAt":"2026-03-23 10:39:58","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9199322/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9199322/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106960807,"identity":"5a82f2e1-1e59-4853-87cd-352da0c7d45c","added_by":"auto","created_at":"2026-04-15 09:23:13","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":711335,"visible":true,"origin":"","legend":"","description":"","filename":"Dynamicequilibriumstabilityandsensitivityanalysisofanthropogenicmetalcycleswithanapplicationtocopper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9199322/v1_covered_f4adb025-697e-47bb-97ae-924c62405225.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dynamic equilibrium, stability and sensitivity analysis of anthropogenic metal cycles with an application to copper","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":"anthropogenic metal cycles, dynamical systems, stability analysis, copper, material flow analysis, sensitivity analysis","lastPublishedDoi":"10.21203/rs.3.rs-9199322/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9199322/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Anthropogenic metal cycles shape resource availability, recycling performance and long-term sustainability: understanding their dynamic behaviour, including long-term stability and sensitivity to change, is essential for sustainable resource management and supply-chain resilience. 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