  We investigate the dynamics of large-scale interacting neural populations,
composed of conductance based, spiking model neurons with modifiable synaptic
connection strengths, which are possibly also subjected to external noisy
currents. The network dynamics is controlled by a set of neural population
probability distributions ($\mathrm{PPD}$)which are constructed along the same
lines as in the Klimontovich approach to the kinetic theory of plasmas. An
exact non-closed, nonlinear, system of integro-partial differential equations
is derived for the $\mathrm{PPD}$s. As is customary, a closing procedure leads
to a mean field limit. The equations we have obtained are of the same type as
those which have been recently derived using rigorous techniques of probability
theory. The numerical solutions of these so called McKean-Vlasov-Fokker-Planck
equations, which are only valid in the limit of infinite size networks,
actually shows that the statistical measures as obtained from $\mathrm{PPD}$s
are in good agreement with those obtained through direct integration of the
stochastic dynamical system for large but finite size networks. Although
numerical solutions have been obtained in the case of Fitzhugh-Nagumo model
neurons, the theory can be readily applied to systems of Hodgkin-Huxley type
model neurons of arbitrary dimension.
