Canard cascading in networks with adaptive mean-field coupling

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dc.contributor.authorBalzer, J.en
dc.contributor.authorBerner, R.en
dc.contributor.authorLüdge, K.en
dc.contributor.authorWieczorek, Sebastianen
dc.contributor.authorKurths, J.en
dc.contributor.authorYanchuk, Serhiyen
dc.contributor.funderDeutsche Forschungsgemeinschaften
dc.date.accessioned2025-01-15T12:17:59Z
dc.date.available2025-01-15T12:17:59Z
dc.date.issued2024-12-02en
dc.description.abstractCanard cascading (CC) is observed in dynamical networks with global adaptive coupling. It is a slow-fast phenomenon characterized by a recurrent sequence of fast transitions between distinct and slowly evolving quasistationary states. In this Letter, we uncover the dynamical mechanisms behind CC, using an illustrative example of globally and adaptively coupled semiconductor lasers, where CC represents sequential switching on and off the lasers. First, we show that CC is a robust and truly adaptive network effect that is scalable with network size and does not occur without adaptation. Second, we uncover multiple saddle slow manifolds (unstable quasistationary states) linked by heteroclinic orbits (fast transitions) in the phase space of the system. This allows us to identify CC with a novel heteroclinic canard orbit that organizes different unstable quasistationary states into an intricate slow-fast limit cycle. Although individual quasistationary states are unstable (saddles), the CC cycle as a whole is attractive and robust to parameter changes.en
dc.description.sponsorshipDeutsche Forschungsgemeinschaft (Project 411803875)en
dc.description.statusPeer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.articleid237401en
dc.identifier.citationBalzer, J., Berner, R., Lüdge, K., Wieczorek, S., Kurths, J. and Yanchuk, S. (2024) 'Canard cascading in networks with adaptive mean-field coupling', Physical Review Letters, 133(23), 237401 (7pp). https://doi.org/10.1103/physrevlett.133.237401en
dc.identifier.doi10.1103/physrevlett.133.237401en
dc.identifier.eissn1079-7114en
dc.identifier.endpage7en
dc.identifier.issn0031-9007en
dc.identifier.issued23en
dc.identifier.journaltitlePhysical Review Lettersen
dc.identifier.startpage1en
dc.identifier.urihttps://hdl.handle.net/10468/16827
dc.identifier.volume133en
dc.language.isoenen
dc.publisherAmerican Physical Societyen
dc.relation.ispartofPhysical Review Lettersen
dc.rights© 2024, American Physical Society. All rights reserved.en
dc.subjectHeteroclinic canard orbiten
dc.subjectCanard cascading (CC)en
dc.titleCanard cascading in networks with adaptive mean-field couplingen
dc.typeArticle (peer-reviewed)en
oaire.citation.issue23en
oaire.citation.volume133en
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