Mean-Field Theory of Irregularly Spiking Neuronal Populations and Working Memory in Recurrent Cortical Networks - Computational Neuroscience: A Comprehensive Approach - page 425

Chapter 15

Mean-FieldTheoryof
Irregularly Spiking Neuronal
PopulationsandWorking
MemoryinRecurrentCortical
Networks

Alfonso Renart, 1 Nicolas Brunel, 2 and Xiao-Jing Wang 1
1 Volen Center for Complex Systems, Brandeis University, Waltham, MA 02254,
U.S., 2 CNRS, Neurophysique et Physiologie du Systeme Moteur, Universit´eParis
Rene Descartes, 45 rue des Saints Peres, 75270 Paris Cedex 06, France

CONTENTS
15.1 Introduction
15.2 Firing-rate and variability of a spiking neuron with noisy input
15.2.1 Theleakyintegrate-and-fireneuron
15.2.2 Temporalstructureoftheafferentsynapticcurrent
15.2.3 Thediffusionapproximation
15.2.4 ComputationofthemeanfiringrateandCV
15.2.5 Effectofsynaptictimeconstants
15.2.6 Approximate treatment of realistic synaptic dynamics
15.3 Self-consistenttheoryofrecurrentcorticalcircuits
15.3.1 Self-consistent steady-state solutions in large unstructured net-
works
15.3.2 Stability and dynamics
15.3.3 Bistability in a single population network
15.3.4 Persistent neural activity in an object working memory model

15.3.5 Stability of the persistent activity state
15.3.6 Multistability in balanced networks
15.4 Summaryandfuturedirections
Appendix1: Thediffusionapproximation
Appendix 2: Stability of the steady-state solutions for r ss (

V )

References