title: Synchrony and asynchrony for neuronal dynamics defined on complex networks.
abstract: 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 (Erdős-Rényi) 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.
authors.affiliation: University of Illinois, Urbana, IL 60801, USA. rdeville@illinois.edu
authors.forename: R E Lee
authors.initials: RE
authors.lastname: Deville
authors.forename: Charles S
authors.initials: CS
authors.lastname: Peskin
mesh_terms: D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D013269:Stochastic Processes