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A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

Schaffer, Evan S.; Ostojic, Srdjan; Abbott, Larry

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.


Also Published In

PLOS Computational Biology

More About This Work

Academic Units
Physiology and Cellular Biophysics
Published Here
November 18, 2016