Singular basins in multiscale systems

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dc.contributor.authorYanchuk, Serhiy
dc.contributor.authorWieczorek, Sebastian
dc.contributor.authorJardón-Kojakhmetov, Hildeberto
dc.contributor.authorAlkhayuon, Hassan
dc.date.accessioned2026-02-11T14:50:01Z
dc.date.available2026-02-11T14:50:01Z
dc.date.issued2026-01-05
dc.description.abstractReal-world complex systems often evolve on different timescales and possess multiple coexisting stable states. Whether or not a system returns to a given stable state after being perturbed away from it depends on the shape and extent of its basin of attraction. In this Letter, we show that basins of attraction in multiscale systems can exhibit special geometric properties in the form of universal singular funnels. We use the term singular basins to refer to basins of attraction with singular funnels. We show that singular basins occur robustly in a range of dynamical systems: the normal form of a pitchfork bifurcation with a slowly changing parameter, an adaptive active rotator, and an adaptive network of phase rotators. Although singular funnels are narrow, they can extend to different parts of the phase space and, unexpectedly, impact the resilience of the system to disturbances. Crucially, the presence of a singular funnel may prevent the usual dimensionality reductions in the limit of large timescale separation, such as quasi-static approximation, adiabatic elimination or time-averaging of the fast variablesen
dc.description.sponsorshipThis work emanated from the research funded by Taighde Éirean.
dc.format.extent13
dc.format.mimetypeapplication/pdfen
dc.identifier.authororcidYanchuk, Serhiy§0000-0003-1628-9569
dc.identifier.authororcidWieczorek, Sebastian§0000-0003-0090-7836
dc.identifier.authororcidJardón-Kojakhmetov, Hildeberto
dc.identifier.authororcidAlkhayuon, Hassan§0000-0001-8117-4907
dc.identifier.citationYanchuk, S, Wieczorek, S, Jardón-Kojakhmetov, H & Alkhayuon, H 2026 'Singular basins in multiscale systems' arXiv, pp. 1-13.
dc.identifier.endpage13
dc.identifier.otherArXiv: http://arxiv.org/abs/2601.02001v1
dc.identifier.otherORCID: /0000-0003-1628-9569/work/205466649
dc.identifier.otherORCID: /0000-0001-8117-4907/work/205466734
dc.identifier.startpage1
dc.identifier.urihttps://hdl.handle.net/10468/18514
dc.language.isoen
dc.publisherarXiv
dc.rights© 2026, the authors.
dc.rights.accessrightsopen access
dc.subjectMath.DS
dc.subjectMath-ph
dc.subjectNlin.AO
dc.subject[Maths]
dc.titleSingular basins in multiscale systemsen
dc.typeArticle (preprint)
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