 
Summary: The PSTH response to spike input as predicted by an expansion of a
population equation
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Models of the activity of a population of many neurons are a central
component for the understanding of cortical dynamics.
An equation that describes the populationaveraged firing rate of a
network of Poisson neurons with absolute refractoriness was already
given by Wilson and Cowan [1]. Many studies have built on their
pioneering work [2, 3], and have tried to give an accurate and realistic
model that is also analytically tractable. Here we adopt the approach
described in [2], in which a population of neurons, modeled as a spike
response model [2], is considered. The population receives a weak
current perturbation that results in an input perturbation which
eventually leads to a deviation of the population activity, A(t). An
equation is derived that gives the deviation in A(t) as a function of the
input perturbations. See Eq. (1) (All equations are given in the
Appendix).
This equation is exact in the limit of an infinite number of neurons and
weak perturbations. We will refer to solution of the population activity,
A(t), as given by this equation (Eq. 1) as "the full dynamics".
