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In this paper, we consider the generalized Hodgkin-Huxley model introduced byAustin in \cite{Austin}. This model describes the propagation of an actionpotential along the axon of a neuron at the scale of ion channels.Mathematically, this model is a fully-coupled Piecewise Deterministic MarkovProcess (PDMP) in infinite dimension. We introduce two time scales in thismodel in considering that some ion channels open and close at faster jump ratesthan others. We perform a slow-fast analysis of this model and prove thatasymptotically this two time scales model reduces to the so called averagedmodel which is still a PDMP in infinite dimension for which we provideeffective evolution equations and jump rates.

Averaging for a Fully-Coupled Piecewise Deterministic Markov Process in Infinite Dimension