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Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks

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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.

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  1. University of Illinois, 1609 W. Green St., Urbana, IL, 60801, USA

    R. E. Lee DeVille

  2. Courant Institute, 251 Mercer St., New York, NY, 10012, USA

    Charles S. Peskin

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  1. R. E. Lee DeVille
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DeVille, R.E.L., Peskin, C.S. Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks. Bull Math Biol 74, 769–802 (2012). https://doi.org/10.1007/s11538-011-9674-0

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