Stochasticity in localized synfire chain

We report on stochastic evolutions of firing states through feedforward neural networks with Mexican-Hat-type connectivity. The variance in connectivity, which depends on the pre-synaptic neuron, generates a common noisy input to post-synaptic neurons. We develop a theory to describe the stochastic evolution of the localized synfire chain driven by a common noisy input. The development of a firing state through neural layers does not converge to a certain fixed point but keeps on fluctuating. Stationary firing states except for a non-firing state are lost, but an almost stationary distribution of firing state is observed.