Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks
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- 作者：R. E. Lee DeVille (1) rdeville@illinois.edu
Charles S. Peskin (2) - 关键词：Neural network – ; Neuronal network – ; Synchrony – ; Mean ; field analysis – ; Stochastic integrate ; and ; fire – ; Random graphs – ; Scale ; free networks – ; Small world networks – ; Complex networks – ; Erdő ; s– ; R
- 刊名：Bulletin of Mathematical Biology
- 出版时间：April 2012
- 出版年：2012
- 期刊代码：131_1522-9602
- 类别：mat
- 卷：74
- 期：4
- 页码：769-802
- 数据来源：sp
摘要
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–R茅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.