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  <doc>
    <id>10110</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
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    <title language="eng">Unfolding the geometric structure and multiple timescales of the urea-urease pH oscillator</title>
    <abstract language="eng">We study a two-variable dynamical system modeling pH oscillations in the urea–urease reaction within giant lipid vesicles – a problem that intrinsically contains multiple, well-separated timescales. Building on an existing, deterministic formulation via ordinary differential equations, we resolve different orders of magnitude within a small parameter and analyze the system's limit cycle behavior using geometric singular perturbation theory (GSPT). By introducing two different coordinate scalings – each valid in a distinct region of the phase space – we resolve the local dynamics near critical fold points, using the extension of GSPT through such singular points due to Krupa and Szmolyan. This framework enables a geometric decomposition of the periodic orbits into slow and fast segments and yields closed-form estimates for the period of oscillation. In particular, we link the existence of such oscillations to an underlying biochemical asymmetry, namely, the differential transport across the vesicle membrane.</abstract>
    <identifier type="arxiv">2508.07275</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="PeerReviewed">no</enrichment>
    <submitter>Arthur Straube</submitter>
    <author>Arthur Straube</author>
    <author>Guillermo Olicón Méndez</author>
    <author>Stefanie Winkelmann</author>
    <author>Felix Höfling</author>
    <author>Maximilian Engel</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="hoefling">Höfling, Felix</collection>
    <collection role="persons" number="straube">Straube, Arthur</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="PaDC">Parallel and Distributed Computing</collection>
    <collection role="projects" number="MathPlusAA1-18">MathPlusAA1-18</collection>
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