Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks

R. E.Lee DeVille, Charles S. Peskin

Research output: Contribution to journalArticlepeer-review


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 (Erdos-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.

Original languageEnglish (US)
Pages (from-to)769-802
Number of pages34
JournalBulletin of Mathematical Biology
Issue number4
StatePublished - Apr 2012


  • Complex networks
  • Erdos-Rényi
  • Mean-field analysis
  • Neural network
  • Neuronal network
  • Random graphs
  • Scale-free networks
  • Small world networks
  • Stochastic integrate-and-fire
  • Synchrony

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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