In this paper we study the synchronization of a stochastically-driven, current-based, integrate-and-fire neuronal model on a preferential-attachment network with scale-free characteristics and high clustering through cascading total firing events where every neuron in the network fires at the same instant of time. We show that in the regime where the system remains in this highly synchronous state, the firing rate of the network is fully described by the external drive. On the other hand, the probability for the network to maintain synchronized depends on a balance between the fluctuations of the external input and the synaptic coupling strength. In order to accurately predict the probability to see repeated cascading total firing events we must include a description of the local network topology around one node, and not just the degree distribution. We compare our fully analytical results for a particular preferential-attachment network to direct numerical simulations.

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This work was partly supported by the National Science Foundation through grants DMS-0506287 and and DMS-0636358.

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