Bifurcation of critical sets and relaxation oscillations in singular fast-slow systems
dc.contributor.author | Nyman, K | |
dc.contributor.author | Ashwin, P | |
dc.contributor.author | Ditlevsen, P | |
dc.date.accessioned | 2020-01-29T11:51:09Z | |
dc.date.issued | 2020-04-14 | |
dc.description.abstract | Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the fast subsystem) and associated fast dynamics, parametrized by the slow variables. Using a distinguished parameter approach we are able to classify bifurcations for one fast and one slow variable. Some of these bifurcations are associated with the critical set losing manifold structure. We also conjecture a list of generic bifurcations of the critical set for one fast and two slow variables. We further consider how the bifurcations of the critical set can be associated with generic bifurcations of attracting relaxation oscillations under an appropriate singular notion of equivalence. | en_GB |
dc.description.sponsorship | European Commission | en_GB |
dc.identifier.citation | Vol. 33 (6), pp. 2853–2904 | en_GB |
dc.identifier.doi | 10.1088/1361-6544/ab7292 | |
dc.identifier.grantnumber | EP/M017915/1 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/40640 | |
dc.language.iso | en | en_GB |
dc.publisher | IOP Publishing / London Mathematical Society | en_GB |
dc.rights | © 2020 IOP Publishing Ltd & London Mathematical Society. Open access. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. | |
dc.subject | Fast-slow dynamics | en_GB |
dc.subject | Relaxation oscillation | en_GB |
dc.subject | Bifurcation | en_GB |
dc.subject | Singularity | en_GB |
dc.title | Bifurcation of critical sets and relaxation oscillations in singular fast-slow systems | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2020-01-29T11:51:09Z | |
dc.identifier.issn | 0951-7715 | |
dc.description | This is the final version. Available on open access from IOP Publishing via the DOI in this record | en_GB |
dc.identifier.journal | Nonlinearity | en_GB |
dc.rights.uri | https://creativecommons.org/licenses/by/3.0/ | en_GB |
dcterms.dateAccepted | 2020-02-03 | |
exeter.funder | ::European Commission | en_GB |
rioxxterms.version | VoR | en_GB |
rioxxterms.licenseref.startdate | 2020-01-29 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2020-01-29T11:24:35Z | |
refterms.versionFCD | AM | |
refterms.dateFOA | 2020-05-19T15:14:41Z | |
refterms.panel | B | en_GB |
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attribution to the author(s) and the title of the work, journal citation and DOI.