  Spike propagation for spatially correlated inputs in layered neural networks
has been investigated with the use of a semi-analytical dynamical mean-field
approximation (DMA) theory recently proposed by the author [H. Hasegawa, Phys.
Rev. E {\bf 67}, 041903 (2003)]. Each layer of the network is assumed to
consist of FitzHugh-Nagumo neurons which are coupled by feedforward couplings.
Applying single spikes to the network with input-time jitters whose
root-mean-square (RMS) value and the spatial correlation are $\sigma_I$ and
$s_I$, respectively, we have calculated the RMS value ($\sigma_{Om}$) and the
correlation ($s_{Om}$) of jitters in output-firing times on each layer $m$. For
all-to-all feedforward couplings, $s_{Om}$ gradually grows to a fairly large
value as spikes propagate through the layer, even for inputs without the
correlation. This shows that for the correlation to be in the range of observed
value of 01-0.3, we have to take into account noises and more realistic
feedforward couplings. Model calculations including local feedforward
connection besides all-to-all feedforward couplings in multilayers subject to
white noises, have shown that in a long multilayer, $\sigma_{Om}$ and $s_{Om}$
converge to fixed-point values which are determined by model parameters
characterizing the multilayer architecture. Results of DMA calculations are in
fairly good agreement with those of direct simulations although the
computational time of the former is much smaller than that of the latter.
