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Abstract:
Mesoscopical, mathematical descriptions of dynamics of
populations of spiking neurons are getting increasingly important
for the understanding of large-scale processes in the brain using
simulations. In our previous work, integral equation formulations
for population dynamics have been derived for a special type of
spiking neurons. For Integrate-and-Fire type neurons, these
formulations were only approximately correct. Here, we derive a
mathematically compact, exact population dynamics formulation for
Integrate-and-Fire type neurons. It can be shown quantitatively
in simulations that the numerical correspondence with
microscopically modeled neuronal populations is excellent.
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