Spatio-temporal averaging for a class of hybrid systems. Application to conductance-based neuron models (1403.1751v2)

Abstract: We obtain a limit theorem endowed with quantitative estimates for a general class of infinite dimensional hybrid processes with intrinsically two different time scales and including a population. As an application, we consider a large class of conductance-based neuron models describing the nerve impulse propagation along a neural cell at the scales of ion channels.