<div class="csl-bib-body">
<div class="csl-entry">Jelbart, S. I. (2024, June 25). <i>Critical transitions in asymptotically slow-fast systems</i> [Conference Presentation]. Biennial Congress of the Spanish Society of Applied Mathematics SeMA (2024), Bilbao, Spain.</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/199576
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dc.description.abstract
We discuss a geometric approach to the study of bifurcation and rate induced transitions in a class of asymptotically slow-fast systems, which are in some sense ‘intermediate’ between the (smaller resp. larger) classes of asymptotically autonomous and non-autonomous systems. After showing that the relevant systems can be viewed as singular perturbations of a limiting system with a discontinuity in time, we consider an analytical framework for their analysis based on geometric blow-up techniques. Using this approach, we provide sufficient conditions for the occurrence of bifurcation and rate induced transitions in low dimensions, as well as sufficient conditions for tracking in arbitrary (finite) dimensions, i.e. the persistence of an attracting and normally hyperbolic manifold through the transitionary regime. The proofs rely on geometric blow-up, a variant of the Melnikov method which applies on non-compact domains, and general invariant manifold theory. We conclude by applying these results to a low-dimensional problem with forward and backward attractors that feature slow but non-constant dependence on time.
en
dc.language.iso
en
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dc.subject
Critical Transitions
en
dc.subject
Non-autonomous Dynamical Systems
en
dc.subject
Tipping
en
dc.title
Critical transitions in asymptotically slow-fast systems
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Conference Presentation
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E101-01 - Forschungsbereich Analysis
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tuw.author.orcid
0000-0001-8539-320X
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tuw.event.name
Biennial Congress of the Spanish Society of Applied Mathematics SeMA (2024)
en
tuw.event.startdate
24-06-2024
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tuw.event.enddate
28-06-2024
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Bilbao
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tuw.event.country
ES
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tuw.event.institution
Spanish Society of Applied Mathematics
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tuw.event.presenter
Jelbart, Samuel Isaac
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.grantfulltext
none
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item.languageiso639-1
en
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairetype
conference paper not in proceedings
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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crisitem.author.dept
E101-01 - Forschungsbereich Analysis
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crisitem.author.orcid
0000-0001-8539-320X
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crisitem.author.parentorg
E101 - Institut für Analysis und Scientific Computing
