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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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| Published in: | Bulletin of mathematical biology 2012-04, Vol.74 (4), p.769-802 |
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| container_title | Bulletin of mathematical biology |
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| creator | DeVille, R. E. Lee Peskin, Charles S. |
| description | 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. |
| doi_str_mv | 10.1007/s11538-011-9674-0 |
| format | article |
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E. Lee ; Peskin, Charles S.</creator><creatorcontrib>DeVille, R. E. Lee ; Peskin, Charles S.</creatorcontrib><description>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. 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| 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 |
| title | Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks |
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