  We report on a novel type of instability observed in a noisy oscillator
unidirectionally coupled to a pacemaker. Using a phase oscillator model, we
find that, as the coupling strength is increased, the noisy oscillator lags
behind the pacemaker more frequently and the phase slip rate increases, which
may not be observed in averaged phase models such as the Kuramoto model.
Investigation of the corresponding Fokker-Planck equation enables us to obtain
the reentrant transition line between the synchronized state and the phase slip
state. We verify our theory using the Brusselator model, suggesting that this
reentrant transition can be found in a wide range of limit cycle oscillators.
