Reversible Saddle-Node Separatrix-Loop bifurcation

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dc.check.date2026-03-17en
dc.check.infoAccess to this article is restricted until 12 months after publication by request of the publisheren
dc.contributor.authorBurylko, Oleksandren
dc.contributor.authorWolfrum, Matthiasen
dc.contributor.authorYanchuk, Serhiyen
dc.contributor.editorTimokha, Alexanderen
dc.contributor.funderDeutsche Forschungsgemeinschaften
dc.contributor.funderNational Research Foundation of Ukraineen
dc.date.accessioned2025-04-29T09:28:46Z
dc.date.available2025-04-29T09:28:46Z
dc.date.issued2025-03-17en
dc.description.abstractWe describe the unfolding of a special variant of the codimension-two Saddle-Node Separatrix-Loop (SNSL) bifurcation that occurs in systems with time-reversibility. While the classical SNSL bifurcation can be characterized as the collision of a saddle-node equilibrium with a limit cycle, the reversible variant (R-SNSL) is characterised by as the collision of a saddle-node equilibrium with a boundary separating a dissipative and a conservative region in phase space. Moreover, we present several reversible versions of the SNIC (Saddle-Node on Invariant Circle) bifurcation and discuss the role of an additional reversible saddle equilibrium in all these scenarios. As an example, we provide a detailed bifurcation scenario for a reversible system of two coupled phase rotators (a system on a 2D torus) involving a R-SNSL bifurcation.en
dc.description.sponsorshipNational Research Foundation of Ukraine (Project 2020.02/0089); Deutsche Forschungsgemeinschaft (Project 411803875; Project 195170736 - SFB/TRR 109; Project 211504053 - SFB 1060)en
dc.description.statusPeer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationBurylko, O., Wolfrum, M. and Yanchuk, S. (2025) 'Reversible Saddle-Node Separatrix-Loop bifurcation', in Timokha, A. (ed) Analytical and Approximate Methods for Complex Dynamical Systems. Understanding Complex Systems. Springer, Cham. p. 101–119. https://doi.org/10.1007/978-3-031-77378-5_7en
dc.identifier.doi10.1007/978-3-031-77378-5_7en
dc.identifier.eissn1860-0840en
dc.identifier.endpage119en
dc.identifier.isbn9783031773778en
dc.identifier.isbn9783031773785en
dc.identifier.issn1860-0832en
dc.identifier.startpage101en
dc.identifier.urihttps://hdl.handle.net/10468/17352
dc.language.isoenen
dc.publisherSpringer Natureen
dc.relation.ispartofUnderstanding Complex Systemsen
dc.relation.ispartofAnalytical and Approximate Methods for Complex Dynamical Systemsen
dc.relation.ispartofseriesUnderstanding Complex Systemsen
dc.rights© 2025, The Authors, under exclusive license to Springer Nature Switzerland AG. This version of the paper has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/978-3-031-77378-5_7en
dc.subjectSaddle-Node Separatrix-Loopen
dc.subjectBifurcationen
dc.subjectSaddle-Node on Invariant Circleen
dc.subjectTime-reversibilityen
dc.subjectCoupled rotatorsen
dc.subjectR-SNSLen
dc.subjectCodimension-twoen
dc.subjectSNICen
dc.titleReversible Saddle-Node Separatrix-Loop bifurcationen
dc.typeBook chapteren
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