A complex-valued firing-rate model that approximates the dynamics of spiking networks.

• Main Authors: Evan S Schaffer, Srdjan Ostojic, L F Abbott
• Format: Article
• Language: English
• Published: Public Library of Science (PLoS) 2013-10-01
• Series: PLoS Computational Biology
• Online Access: http://europepmc.org/articles/PMC3814717?pdf=render

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.