Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks

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 s...

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Bibliographic Details
Published in:Bulletin of mathematical biology 2012-04, Vol.74 (4), p.769-802
Main Authors: DeVille, R. E. Lee, Peskin, Charles S.
Format: Article
Language:English
Subjects:
Cell Biology
Computer Simulation
Humans
Life Sciences
Mathematical and Computational Biology
Mathematical models
Mathematics
Mathematics and Statistics
Models, Neurological
Nerve Net - physiology
Neurons - physiology
Original Article
Stochastic Processes
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Summary: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.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-011-9674-0