Neuronal coding of pacemaker neurons -- A random dynamical    systems approach

T. Jäger

doi:10.3934/cpaa.2011.10.995

Article Contents

2011, Volume 10, Issue 3: 995-1009. Doi: 10.3934/cpaa.2011.10.995

This issue Previous Article A note on almost periodic variational equations Next Article

Neuronal coding of pacemaker neurons -- A random dynamical systems approach

T. Jäger^1,

1.
Institut für Analysis, TU Dresden, 01219 Dresden

Received: February 28, 2009

Revised: August 31, 2009

Published: April 2011

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Abstract

The behaviour of neurons under the influence of periodic external input has been modelled very successfully by circle maps. The aim of this note is to extend certain aspects of this analysis to a much more general class of forcing processes. We apply results on the fibred rotation number of randomly forced circle maps to show the uniqueness of the asymptotic firing frequency of ergodically forced pacemaker neurons. In particular, this allows to treat the forced leaky integrate-and-fire model, which serves as a paradigm example.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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