  We study the reliability of phase oscillator networks in response to
fluctuating inputs. Reliability means that an input elicits essentially
identical responses upon repeated presentations, regardless of the network's
initial condition. In this paper, we extend previous results on two-cell
networks to larger systems. The first issue that arises is chaos in the absence
of inputs, which we demonstrate and interpret in terms of reliability. We give
a mathematical analysis of networks that can be decomposed into modules
connected by an acyclic graph. For this class of networks, we show how to
localize the source of unreliability, and address questions concerning
downstream propagation of unreliability once it is produced.
