Journal of Statistical Physics, Vol. 67, Nos. 1/2, 1992, p. 313-330.
A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution is bimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and their nonlinear stability properties ascertained.