Journal of Mathematical Biology

, Volume 78, Issue 1–2, pp 83–115 | Cite as

How well do reduced models capture the dynamics in models of interacting neurons?

  • Yao Li
  • Logan Chariker
  • Lai-Sang YoungEmail author


This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations. Rigorous results on existence and uniqueness of nonequilibrium steady states are proved. These network models are then compared to very simple reduced models driven by the same mean excitatory and inhibitory currents. Discrepancies in firing rates between network and reduced models are investigated and explained by correlations in spiking, or partial synchronization, working in concert with “nonlinearities” in the time evolution of membrane potentials. The use of simple random walks and their first passage times to simulate fluctuations in neuronal membrane potentials and interspike times is also considered.

Mathematics Subject Classification

92B99 92C42 60J28 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Massachusetts AmherstAmherstUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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