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


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.


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



JZ is partially supported by NSF Grant DMS-1009575. AR is supported by NSF Grants DMS-0914827 and DMS/NIGMS-1162548. DZ is supported by Shanghai Pujiang Program (Grant No. 10PJ1406300), NSFC (Grant No. 11101275 and No. 91230202) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars from State Education Ministry in China. DC is supported by NSF Grant DMS-1009575. DZ and DC are supported by New York University Abu Dhabi Research Grant G1301.

Conflict of interests

The authors declare that they have no conflict of interest.

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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