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We show how the Equation-Free approach for mutliscale computations can beexploited to extract, in a computational strict and systematic way the emergentdynamical attributes, from detailed large-scale microscopic stochastic models,of neurons that interact on complex networks. In particular we show how theEquation-Free approach can be exploited to perform system-level tasks such asbifurcation, stability analysis and estimation of mean appearance times of rareevents, bypassing the need for obtaining analytical approximations, providingan "on-demand" model reduction. Using the detailed simulator as a black-boxtimestepper, we compute the coarse-grained equilibrium bifurcation diagrams,examine the stability of the solution branches and perform a rare-eventsanalysis with respect to certain characteristics of the underlying networktopology such as the connectivity degree

Coarse-Grained Analysis of Microscopic Neuronal Simulators on Networks: Bifurcation and Rare-events computations