  It is known that an identical delay in all transmission lines can destabilize
macroscopic stationarity of a neural network, causing oscillation or chaos. We
analyze the collective dynamics of a network whose intra-transmission delays
are distributed in time. Here, a neuron is modeled as a discrete-time threshold
element that responds in an all-or-nothing manner to a linear sum of signals
that arrive after delays assigned to individual transmission lines. Even though
transmission delays are distributed in time, a whole network exhibits a single
collective oscillation with a period close to the average transmission delay.
The collective oscillation can not only be a simple alternation of the
consecutive firing and resting, but also nontrivially sequenced series of
firing and resting, reverberating in a certain period of time. Moreover, the
system dynamics can be made quasiperiodic or chaotic by changing the
distribution of delays.
