title: A complex-valued firing-rate model that approximates the dynamics of spiking networks.
abstract: 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.
authors.affiliation: Department of Neuroscience, Department of Physiology and Cellular Biophysics, Columbia University College of Physicians and Surgeons, New York, New York, United States of America.
authors.forename: Evan S
authors.initials: ES
authors.lastname: Schaffer
authors.forename: Srdjan
authors.initials: S
authors.lastname: Ostojic
authors.forename: L F
authors.initials: LF
authors.lastname: Abbott
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D019295:Computational Biology; D003198:Computer Simulation; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology