  A model of globally coupled phase oscillators under equilibrium (driven by
Gaussian white noise) and nonequilibrium (driven by symmetric dichotomic
fluctuations) is studied. For the equilibrium system, the mean-field state
equation takes a simple form and the stability of its solution is examined in
the full space of order parameters. For the nonequilbrium system, various
asymptotic regimes are obtained in a closed analytical form. In a general case,
the corresponding master equations are solved numerically. Moreover, the
Monte-Carlo simulations of the coupled set of Langevin equations of motion is
performed. The phase diagram of the nonequilibrium system is presented. For the
long time limit, we have found four regimes. Three of them can be obtained from
the mean-field theory. One of them, the oscillating regime, cannot be predicted
by the mean-field method and has been detected in the Monte-Carlo numerical
experiments.
