A reduction for spiking integrate-and-fire network dynamics ranging from homogeneity to synchrony

J. W. Zhang, A. V. Rangan

Research output: Contribution to journalArticle


In this paper we provide a general methodology for systematically reducing the dynamics of a class of integrate-and-fire networks down to an augmented 4-dimensional system of ordinary-differential-equations. The class of integrate-and-fire networks we focus on are homogeneously-structured, strongly coupled, and fluctuation-driven. Our reduction succeeds where most current firing-rate and population-dynamics models fail because we account for the emergence of ‘multiple-firing-events’ involving the semi-synchronous firing of many neurons. These multiple-firing-events are largely responsible for the fluctuations generated by the network and, as a result, our reduction faithfully describes many dynamic regimes ranging from homogeneous to synchronous. Our reduction is based on first principles, and provides an analyzable link between the integrate-and-fire network parameters and the relatively low-dimensional dynamics underlying the 4-dimensional augmented ODE.

Original languageEnglish (US)
Pages (from-to)355-404
Number of pages50
JournalJournal of Computational Neuroscience
Issue number2
StatePublished - Jan 1 2015



  • Coarse grain
  • Ensemble average
  • Integrate and fire
  • Spiking network

ASJC Scopus subject areas

  • Sensory Systems
  • Cognitive Neuroscience
  • Cellular and Molecular Neuroscience

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