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dc.contributor.authorNowacki, J
dc.contributor.authorOsinga, HM
dc.contributor.authorTsaneva-Atanasova, Krasimira
dc.date.accessioned2016-02-03T14:34:45Z
dc.date.issued2012
dc.description.abstractTransient bursting behaviour of excitable cells, such as neurons, is a common feature observed experimentally, but theoretically, it is not well understood. We analyse a five-dimensional simplified model of after-depolarisation that exhibits transient bursting behaviour when perturbed with a short current injection. Using one-parameter continuation of the perturbed orbit segment formulated as a well-posed boundary value problem, we show that the spike-adding mechanism is a canard-like transition that has a different character from known mechanisms for periodic burst solutions. The biophysical basis of the model gives a natural time-scale separation, which allows us to explain the spike-adding mechanism using geometric singular perturbation theory, but it does not involve actual bifurcations as for periodic bursts. We show that unstable sheets of the critical manifold, formed by saddle equilibria of the system that only exist in a singular limit, are responsible for the spike-adding transition; the transition is organised by the slow flow on the critical manifold near folds of this manifold. Our analysis shows that the orbit segment during the spike-adding transition includes a fast transition between two unstable sheets of the slow manifold that are of saddle type. We also discuss a different parameter regime where the presence of additional saddle equilibria of the full system alters the spike-adding mechanism.en_GB
dc.description.sponsorshipEngineering and Physical Sciences Research Council (EPSRC)en_GB
dc.identifier.citationVol. 2, art. 7en_GB
dc.identifier.doi10.1186/2190-8567-2-7
dc.identifier.other2190-8567-2-7
dc.identifier.urihttp://hdl.handle.net/10871/19584
dc.language.isoenen_GB
dc.publisherBioMed Centralen_GB
dc.relation.urlhttp://www.ncbi.nlm.nih.gov/pubmed/22655748en_GB
dc.relation.urlhttp://www.mathematical-neuroscience.com/content/2/1/7en_GB
dc.rights© 2012 Nowacki et al.; licensee Springer This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.en_GB
dc.subjectbursten_GB
dc.subjectspike addingen_GB
dc.subjecttransient behaviouren_GB
dc.subjectdynamical systemsen_GB
dc.subjectgeometric singular perturbation theoryen_GB
dc.titleDynamical systems analysis of spike-adding mechanisms in transient burstsen_GB
dc.typeArticleen_GB
dc.date.available2016-02-03T14:34:45Z
dc.identifier.issn2190-8567
pubs.declined2016-02-03T10:51:29.992+0000
exeter.place-of-publicationGermany
dc.descriptionThe electronic version of this article is the complete one and can be found online at: doi:10.1186/2190-8567-2-7en_GB
dc.descriptionOpen Access Articleen_GB
dc.identifier.journalJournal of Mathematical Neuroscienceen_GB
dc.identifier.pmcidPMC3497719
dc.identifier.pmid22655748


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