Journal of Computational Neuroscience

, Volume 36, Issue 2, pp 279–295

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


  • Jiwei Zhang
    • Courant Institute of Mathematical SciencesNew York University
    • Courant Institute of Mathematical SciencesNew York University
  • Douglas Zhou
    • Department of Mathematics, MOE-LSC and Institute of Natural SciencesShanghai Jiao Tong University
  • Aaditya Rangan
    • Courant Institute of Mathematical SciencesNew York University

DOI: 10.1007/s10827-013-0472-6

Cite this article as:
Zhang, J., Newhall, K., Zhou, D. et al. J Comput Neurosci (2014) 36: 279. doi:10.1007/s10827-013-0472-6


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 neuronsSynchronyHomogeneityMultiple firing eventsFirst passage timeIntegrate and fire neuronal networks

Copyright information

© Springer Science+Business Media New York 2013