Canard-Tipping Cascades in adaptive dynamical networks

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dc.check.date2027-12-31
dc.contributor.advisorWieczorek, Sebastian
dc.contributor.advisorYanchuk, Serhiy
dc.contributor.authorLuddy, Adamen
dc.contributor.funderSchool of Computing, Engineering and Mathematical Sciences, La Trobe University
dc.contributor.funderUniversity College Cork
dc.date.accessioned2026-09-29T15:38:32Z
dc.date.available2026-09-29T15:38:32Z
dc.date.issued2026-06-30
dc.date.submitted2026-06-30
dc.description.abstractA tipping point is a strong instability that involves a large, sudden, and often unexpected change in the state of a complex system. A tipping-point cascade is a series of tipping points in a network of coupled systems. Despite their prominence in coupled climate and ecological systems, tipping-point cascades remain largely unexplored. One might naively assume that these cascades always occur between distinct stable states, but this is not necessarily the case. In fact, somewhat counter-intuitively, a network can robustly tip between unstable states during a tipping-point cascade. This type of tipping-point cascade was first seen in the phenomenon of Canard Cascading. In this thesis, we examine non-standard tipping-point cascades in a class of slow-fast adaptive dynamical networks, where robust heteroclinic connections enable a series of fast transitions between coexisting saddle states with slow dynamics. We refer to this novel phenomenon as a Canard-Tipping Cascade (CTC) and demonstrate that it occurs robustly in different networks and for a large set of parameter values. We also relate CTCs to the recently reported phenomenon of Canard Cascading. In particular, we present an ecological example of a CTC: a slow-fast adaptive dynamical network of competitive Lotka--Volterra systems. Furthermore, we discuss candidate equations for the minimal or canonical model exhibiting CTCs in order to gain a better understanding of its fundamental properties. We demonstrate that this canonical model can exhibit both (i) the standard bifurcation-induced tipping (B-tipping) cascade between coexisting alternative stable states and (ii) the non-standard CTC between coexisting saddle states.en
dc.description.statusNot peer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationLuddy, A. 2026. Canard-Tipping Cascades in adaptive dynamical networks. MRes Thesis, University College Cork.
dc.identifier.endpage64
dc.identifier.urihttps://hdl.handle.net/10468/19363
dc.language.isoenen
dc.publisherUniversity College Corken
dc.relation.projectUniversity College Cork (Boole Fellowship)
dc.rights© 2026, Adam Luddy.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectDynamical systems
dc.subjectAdaptive networks
dc.subjectSlow-fast systems
dc.subjectCanards
dc.titleCanard-Tipping Cascades in adaptive dynamical networks
dc.typeMasters thesis (Research)en
dc.type.qualificationlevelMastersen
dc.type.qualificationnameMSc - Master of Scienceen
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