neuron dynamics, new equilibrium, jump in input, exact prediction
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 upward shift in voltage in response to each synaptic event, we compare the theoretical prediction with the result of a direct simulation of 90,000 model neurons. The degree of agreement supports the applicability of the population 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 few terms.
Knight, B.W., Omurtag, A., Sirovich, L. (2000) The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result. Neural Comput. 12, 1045-1055.