The approach of a neuron population firing rate to a new equilibrium: An exact theoretical result

The response of a noninteracting population of identical neurons to a step change in steady synaptic input can be analytically calculated exactly from the dynamical equation that describes the population's evolution in time. Here, for model integrate-and-fire neurons that undergo a fixed finite upwa rd shift in voltage in response to each synaptic event, we compare the theo retical prediction with the result of a direct simulation of 90,000 model n eurons. The degree of agreement supports the applicability of the populatio n dynamics equation. The theoretical prediction is in the form of a series. Convergence is rapid, so that the full result is well approximated by a fe w terms.