A complex-valued firing-rate model that approximates the dynamics of spiking networks.
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2013-10-01
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| Series: | PLoS Computational Biology |
| Online Access: | http://europepmc.org/articles/PMC3814717?pdf=render |
| Summary: | 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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| ISSN: | 1553-734X 1553-7358 |