  We study synchronization phenomenon in a self-correcting population of noisy
phase oscillators with randomly distributed natural frequencies. In our model
each oscillator stochastically switches its phase to the ensemble-averaged
value $\psi$ at a typical rate which is proportional to the degree of phase
coherence $r$. The system exhibits a continuous phase transition to collective
synchronization similar to classical Kuramoto model. Based on the
self-consistent arguments and on the linear stability analysis of an incoherent
state we derive analytically the threshold value $k_c$ of coupling constant
corresponding to the onset of a partially synchronized state. Just above the
transition point the linear scaling law $r\propto k-k_c$ is found. We also show
that nonlinear relation between rate of phase correction and order parameter
leads to non-trivial transition between incoherence and synchrony. To
illustrate our analytical results, numerical simulations have been performed
for a large population of phase oscillators with proposed type of coupling. The
results of this work could become useful in designing distributed networked
systems capable of self-synchronization.
