Journal of Computational Neuroscience

, Volume 37, Issue 1, pp 81–104 | Cite as

A coarse-grained framework for spiking neuronal networks: between homogeneity and synchrony

  • Jiwei Zhang
  • Douglas Zhou
  • David Cai
  • Aaditya V. Rangan
Article

Abstract

Homogeneously structured networks of neurons driven by noise can exhibit a broad range of dynamic behavior. This dynamic behavior can range from homogeneity to synchrony, and often incorporates brief spurts of collaborative activity which we call multiple-firing-events (MFEs). These multiple-firing-events depend on neither structured architecture nor structured input, and are an emergent property of the system. Although these MFEs likely play a major role in the neuronal avalanches observed in culture and in vivo, the mechanisms underlying these MFEs cannot easily be captured using current population-dynamics models. In this work we introduce a coarse-grained framework which illustrates certain dynamics responsible for the generation of MFEs. By using a new kind of ensemble-average, this coarse-grained framework can not only address the nucleation of MFEs, but can also faithfully capture a broad range of dynamic regimes ranging from homogeneity to synchrony.

Keywords

Spiking neurons Synchrony Homogeneity Multiple firing events Partitioned-ensemble-average Dynamical systems 

Supplementary material

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Jiwei Zhang
    • 1
  • Douglas Zhou
    • 2
  • David Cai
    • 1
    • 2
    • 3
  • Aaditya V. Rangan
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Department of Mathematics, MOE-LSC,and Institute of Natural SciencesShanghai Jiao Tong UniversityShanghaiChina
  3. 3.NYUAD InstituteNew York University Abu DhabiAbu DhabiUAE

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