  Based upon the moment closure approach, a Gaussian random field is
constructed to quantitatively and analytically characterize the dynamics of a
random point field. The approach provides us with a theoretical tool to
investigate synchronized spike propagation in a feedforward or recurrent
spiking neural network. We show that the balance between the excitation and
inhibition postsynaptic potentials is required for the occurrence of synfire
chains. In particular, with a balanced network, the critical packet size of
invasion and annihilation is observed. We also derive a sufficient analytic
condition for the synchronization propagation in an asynchronous environment,
which further allows us to disclose the possibility of spatial synaptic
structure to sustain a stable synfire chain. Our findings are in good agreement
with simulations and help us understand the propagation of spatio-temporal
patterns in a random point flied.
