Journal of Computational Neuroscience

, Volume 36, Issue 2, pp 279–295 | Cite as

Distribution of correlated spiking events in a population-based approach for Integrate-and-Fire networks

  • Jiwei Zhang
  • Katherine Newhall
  • Douglas Zhou
  • Aaditya Rangan


Randomly connected populations of spiking neurons display a rich variety of dynamics. However, much of the current modeling and theoretical work has focused on two dynamical extremes: on one hand homogeneous dynamics characterized by weak correlations between neurons, and on the other hand total synchrony characterized by large populations firing in unison. In this paper we address the conceptual issue of how to mathematically characterize the partially synchronous “multiple firing events” (MFEs) which manifest in between these two dynamical extremes. We further develop a geometric method for obtaining the distribution of magnitudes of these MFEs by recasting the cascading firing event process as a first-passage time problem, and deriving an analytical approximation of the first passage time density valid for large neuron populations. Thus, we establish a direct link between the voltage distributions of excitatory and inhibitory neurons and the number of neurons firing in an MFE that can be easily integrated into population–based computational methods, thereby bridging the gap between homogeneous firing regimes and total synchrony.


Spiking neurons Synchrony Homogeneity Multiple firing events First passage time Integrate and fire neuronal networks 



The authors would like to thank David Cai for useful discussions. J. Z. is partially supported by NSF grant DMS-1009575, K. N. is supported by the Courant Institute. D. Z. is supported by Shanghai Pujiang Program (Grant No. 10PJ1406300), NSFC (Grant No. 11101275 and No. 91230202), as well as New York University Abu Dhabi Research Grant G1301. A. R. is supported by NSF Grant DMS-0914827.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Jiwei Zhang
    • 1
  • Katherine Newhall
    • 1
  • Douglas Zhou
    • 2
  • Aaditya 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

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