Neuronal Coding of pacemaker neurons - A random dynamical systems approach

TL;DR

This paper extends the analysis of neuronal firing models to include more general random forcing processes, demonstrating the uniqueness of firing frequency in ergodically forced pacemaker neurons using a dynamical systems approach.

Contribution

It introduces a novel application of fibred rotation number theory to analyze the firing behavior of neurons under random external inputs.

Findings

Uniqueness of asymptotic firing frequency for ergodically forced neurons

Extension of circle map analysis to more general stochastic forcing

Applicability to a broad class of neuronal models

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. The details of the analysis are carried out for the forced leaky integrate-and-fire model, but the results should also remain valid for a large class of further models.