A showcase of torus canards in neuronal bursters.

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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

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