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

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


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