Synchrony in stochastically driven neuronal networks with complex topologies

Katherine A. Newhall, Maxim S. Shkarayev, Peter R. Kramer, Gregor Kovačič, David Cai

Research output: Contribution to journalArticle

Abstract

We study the synchronization of a stochastically driven, current-based, integrate-and-fire neuronal model on a preferential-attachment network with scale-free characteristics and high clustering. The synchrony is induced by cascading total firing events where every neuron in the network fires at the same instant of time. We show that in the regime where the system remains in this highly synchronous state, the firing rate of the network is completely independent of the synaptic coupling, and depends solely on the external drive. On the other hand, the ability for the network to maintain synchrony depends on a balance between the fluctuations of the external input and the synaptic coupling strength. In order to accurately predict the probability of repeated cascading total firing events, we go beyond mean-field and treelike approximations and conduct a detailed second-order calculation taking into account local clustering. Our explicit analytical results are shown to give excellent agreement with direct numerical simulations for the particular preferential-attachment network model investigated.

Original languageEnglish (US)
Article number052806
JournalPhysical Review E
Volume91
Issue number5
DOIs
StatePublished - May 11 2015

Fingerprint

Neuronal Network
Synchrony
topology
Topology
Preferential Attachment
Clustering
attachment
Instant
Mean Field
Network Model
Neuron
neurons
direct numerical simulation
Synchronization
Integrate
Fluctuations
synchronism
Predict
Approximation
approximation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Newhall, K. A., Shkarayev, M. S., Kramer, P. R., Kovačič, G., & Cai, D. (2015). Synchrony in stochastically driven neuronal networks with complex topologies. Physical Review E, 91(5), [052806]. https://doi.org/10.1103/PhysRevE.91.052806

Synchrony in stochastically driven neuronal networks with complex topologies. / Newhall, Katherine A.; Shkarayev, Maxim S.; Kramer, Peter R.; Kovačič, Gregor; Cai, David.

In: Physical Review E, Vol. 91, No. 5, 052806, 11.05.2015.

Research output: Contribution to journalArticle

Newhall, KA, Shkarayev, MS, Kramer, PR, Kovačič, G & Cai, D 2015, 'Synchrony in stochastically driven neuronal networks with complex topologies', Physical Review E, vol. 91, no. 5, 052806. https://doi.org/10.1103/PhysRevE.91.052806
Newhall, Katherine A. ; Shkarayev, Maxim S. ; Kramer, Peter R. ; Kovačič, Gregor ; Cai, David. / Synchrony in stochastically driven neuronal networks with complex topologies. In: Physical Review E. 2015 ; Vol. 91, No. 5.
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