Homogeneously structured, fluctuation-driven networks of spiking neurons can exhibit a wide variety of dynamical behaviors, ranging from homogeneity to synchrony. We here extend our partitioned-ensemble
average (PEA) formalism to systematically coarse-grain the heterogeneous dynamics of strongly coupled, conductance-based integrate-and-fire neuronal networks. The population dynamics models derived successfully capture the so-called multiple-firing events (MFEs), which emerge naturally in fluctuation-driven networks of strongly coupled neurons. Although these MFEs likely play a crucial role in the generation of the neuronal avalanches observed in vitro and in vivo, the mechanisms underlying these MFEs cannot easily be
understood using standard population dynamic models. Using our PEA formalism, we systematically generate a sequence of model reductions, going from Master equations, to Fokker-Planck equations, and finally, to an augmented system of ordinary differential equations. Furthermore, we show that these reductions can faithfully describe the heterogeneous dynamic regimes underlying the generation of MFEs in strongly coupled conductance-based integrate-and-fire neuronal networks.