dc.contributor.author |
Burke, John |
en |
dc.contributor.author |
Desroches, Mathieu |
en |
dc.contributor.author |
Barry, Anna |
en |
dc.contributor.author |
Kaper, Tasso J |
en |
dc.contributor.author |
Kramer, Mark A |
en |
dc.date.accessioned |
2018-10-16T00:56:08Z |
en |
dc.date.issued |
2012-01 |
en |
dc.identifier.issn |
2190-8567 |
en |
dc.identifier.uri |
http://hdl.handle.net/2292/41944 |
en |
dc.description.abstract |
Rapid action potential generation - spiking - and alternating intervals of spiking and quiescence - bursting - are two dynamic patterns commonly observed in neuronal activity. In computational models of neuronal systems, the transition from spiking to bursting often exhibits complex bifurcation structure. One type of transition involves the torus canard, which we show arises in a broad array of well-known computational neuronal models with three different classes of bursting dynamics: sub-Hopf/fold cycle bursting, circle/fold cycle bursting, and fold/fold cycle bursting. The essential features that these models share are multiple time scales leading naturally to decomposition into slow and fast systems, a saddle-node of periodic orbits in the fast system, and a torus bifurcation in the full system. We show that the transition from spiking to bursting in each model system is given by an explosion of torus canards. Based on these examples, as well as on emerging theory, we propose that torus canards are a common dynamic phenomenon separating the regimes of spiking and bursting activity. |
en |
dc.format.medium |
Electronic |
en |
dc.language |
eng |
en |
dc.relation.ispartofseries |
Journal of mathematical neuroscience |
en |
dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from http://www.sherpa.ac.uk/romeo/issn/2190-8567/ |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.rights.uri |
http://creativecommons.org/licenses/by/2.0 |
en |
dc.title |
A showcase of torus canards in neuronal bursters. |
en |
dc.type |
Journal Article |
en |
dc.identifier.doi |
10.1186/2190-8567-2-3 |
en |
pubs.issue |
1 |
en |
pubs.begin-page |
3 |
en |
pubs.volume |
2 |
en |
dc.rights.holder |
Copyright: The authors |
en |
dc.identifier.pmid |
22657918 |
en |
pubs.publication-status |
Published |
en |
dc.rights.accessrights |
http://purl.org/eprint/accessRights/OpenAccess |
en |
pubs.subtype |
research-article |
en |
pubs.subtype |
Journal Article |
en |
pubs.elements-id |
537437 |
en |
pubs.org-id |
Medical and Health Sciences |
en |
pubs.org-id |
School of Medicine |
en |
pubs.org-id |
Psychological Medicine Dept |
en |
dc.identifier.eissn |
2190-8567 |
en |
pubs.record-created-at-source-date |
2012-06-04 |
en |
pubs.dimensions-id |
22657918 |
en |