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Neural Computation

May 1, 2000, Vol. 12, No. 5, Pages 1045-1055
(doi: 10.1162/089976600300015493)
© 2000 Massachusetts Institute of Technology
The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result
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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.