Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 74, Issue 4, Pages 769-802Publisher
SPRINGER
DOI: 10.1007/s11538-011-9674-0
Keywords
Neural network; Neuronal network; Synchrony; Mean-field analysis; Stochastic integrate-and-fire; Random graphs; Scale-free networks; Small world networks; Complex networks; Erdos-Renyi
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We describe and analyze a model for a stochastic pulse-coupled neuronal network with many sources of randomness: random external input, potential synaptic failure, and random connectivity topologies. We show that different classes of network topologies give rise to qualitatively different types of synchrony: uniform (ErdAs-R,nyi) and small-world networks give rise to synchronization phenomena similar to that in all-to-all networks (in which there is a sharp onset of synchrony as coupling is increased); in contrast, in scale-free networks the dependence of synchrony on coupling strength is smoother. Moreover, we show that in the uniform and small-world cases, the fine details of the network are not important in determining the synchronization properties; this depends only on the mean connectivity. In contrast, for scale-free networks, the dynamics are significantly affected by the fine details of the network; in particular, they are significantly affected by the local neighborhoods of the hubs in the network.
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