Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks

R. E Lee DeVille, Charles Peskin

Research output: Contribution to journalArticle

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 (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
Volume74
Issue number4
DOIs
StatePublished - Apr 2012

Fingerprint

Synaptic Potentials
Synchrony
synchrony
Complex networks
Complex Networks
topology
Synchronization
Topology
Small-world networks
connectivity
Scale-free Networks
Connectivity
Neuronal Network
Small-world Network
Small World
Erdös
Network Topology
Randomness
world

Keywords

  • 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

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

Cite this

Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks. / DeVille, R. E Lee; Peskin, Charles.

In: Bulletin of Mathematical Biology, Vol. 74, No. 4, 04.2012, p. 769-802.

Research output: Contribution to journalArticle

DeVille, R. E Lee ; Peskin, Charles. / Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks. In: Bulletin of Mathematical Biology. 2012 ; Vol. 74, No. 4. pp. 769-802.
@article{c0f75f7141c74cde9bb5cbbd92e7f7d0,
title = "Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks",
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 (Erdos-R{\'e}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.",
keywords = "Complex networks, Erdos-R{\'e}nyi, Mean-field analysis, Neural network, Neuronal network, Random graphs, Scale-free networks, Small world networks, Stochastic integrate-and-fire, Synchrony",
author = "DeVille, {R. E Lee} and Charles Peskin",
year = "2012",
month = "4",
doi = "10.1007/s11538-011-9674-0",
language = "English (US)",
volume = "74",
pages = "769--802",
journal = "Bulletin of Mathematical Biology",
issn = "0092-8240",
publisher = "Springer New York",
number = "4",

}

TY - JOUR

T1 - Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks

AU - DeVille, R. E Lee

AU - Peskin, Charles

PY - 2012/4

Y1 - 2012/4

N2 - 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.

AB - 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.

KW - Complex networks

KW - Erdos-Rényi

KW - Mean-field analysis

KW - Neural network

KW - Neuronal network

KW - Random graphs

KW - Scale-free networks

KW - Small world networks

KW - Stochastic integrate-and-fire

KW - Synchrony

UR - http://www.scopus.com/inward/record.url?scp=84857904402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857904402&partnerID=8YFLogxK

U2 - 10.1007/s11538-011-9674-0

DO - 10.1007/s11538-011-9674-0

M3 - Article

VL - 74

SP - 769

EP - 802

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 4

ER -