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Phase locking in integrate-and-fire models with refractory periods and modulation.

作者信息

Gedeon Tomás, Holzer Matt

机构信息

Department of Mathematical Sciences, Montana State University, Bozeman, MT 59715, USA.

出版信息

J Math Biol. 2004 Dec;49(6):577-603. doi: 10.1007/s00285-004-0268-4. Epub 2004 Mar 3.

DOI:10.1007/s00285-004-0268-4
PMID:15565447
Abstract

It is known [8, 11, 16, 26] that phase locking can entrain frequency information when the leaky integrate-and-fire (IF) model of a neuron is forced by a periodic function. We show that this is still the case when the IF model is made more biologically realistic. We incorporate into our model spike dependent threshold modulation and refractory periods. Consecutive firing times from this model and their respective interspike intervals are related by an annulus map. We prove a general theorem concerning orientation reversing annulus twist homeomorphisms, which shows that our map admits a unique rotation number. This implies, in particular, that chaotic behaviour is not possible in our model and phase locking is predicted.

摘要

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