Show simple item record

dc.contributor.authorDesroches, M. 
dc.contributor.authorKowalczyk, P.
dc.contributor.authorRodrigues, S. 
dc.date.accessioned2021-06-15T20:57:32Z
dc.date.available2021-06-15T20:57:32Z
dc.date.issued2021-05-03
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1296
dc.description.abstractWe study a class of planar integrate and fire (IF) models called adaptive integrate and fire (AIF) models, which possesses an adaptation vari- able on top of membrane potential, and whose subthreshold dynamics is piece- wise linear (PWL). These AIF models therefore have two reset conditions, which enable bursting dynamics to emerge for suitable parameter values. Such models can be thought of as hybrid dynamical systems. We consider a par- ticular slow dynamics within AIF models and prove the existence of bursting cycles with N resets, for any integer N. Furthermore, we study the transition between N- and (N + 1)-reset cycles upon vanishingly small parameter vari- ations and prove (for N = 2) that such transitions are organised by canard cycles. Finally, using numerical continuation we compute branches of bursting cycles, including canard-explosive branches, in these AIF models, by suitably recasting the periodic problem as a two-point boundary-value problem.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.titleSpike-adding and reset-induced canard cycles in adaptive integrate and fire modelsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1007/s11071-021-06441-z
dc.relation.publisherversionhttps://link.springer.com/article/10.1007/s11071-021-06441-zen_US
dc.relation.projectIDES/1PE/SEV-2017-0718en_US
dc.relation.projectIDES/2PE/RTI2018-093860-B-C21en_US
dc.relation.projectIDEUS/BERC/BERC.2018-2021en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US
dc.journal.titleNonlinear Dynamicsen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España