On the simulation of large populations of neurons

The dynamics of large populations of interacting neurons is investigated. R edundancy present in subpopulations of cortical networks is exploited throu gh the introduction of a probabilistic description. A derivation of the kin etic equations for such subpopulations, under general transmembrane dynamic s, is presented. The particular case of integrate-and-fire membrane dynamics is considered i n detail. A variety of direct simulations of neuronal populations, under va rying conditions and with as many as O(10(5)) neurons, is reported. Compari son is made with analogous kinetic equations under the same conditions. Exc ellent agreement, down to fine detail, is obtained. It is emphasized that n o free parameters enter in the comparisons that are made.