  This paper concerns the reliability of a pair of coupled oscillators in
response to fluctuating inputs. Reliability means that an input elicits
essentially identical responses upon repeated presentations regardless of the
network's initial condition. Our main result is that both reliable and
unreliable behaviors occur in this network for broad ranges of coupling
strengths, even though individual oscillators are always reliable when
uncoupled. A new finding is that at low input amplitudes, the system is highly
susceptible to unreliable responses when the feedforward and feedback couplings
are roughly comparable. A geometric explanation based on shear-induced chaos at
the onset of phase-locking is proposed.
