Journal
PLOS COMPUTATIONAL BIOLOGY
Volume 9, Issue 10, Pages -Publisher
PUBLIC LIBRARY SCIENCE
DOI: 10.1371/journal.pcbi.1003301
Keywords
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Funding
- NIH [MH093338]
- Gatsby Foundation
- Swartz Foundation
- Kavli Institute for Brain Science at Columbia University
- European Community
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Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons.
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