  Relationships between inter-cluster synchronization phenomena and external
noise are studied on the basis of noise level-free analysis. We consider a
mean-field model of ensembles of coupled limit cycle oscillators with two
natural frequencies, which are subjected to external white Gaussian noise.
Using a nonlinear Fokker-Planck equation approach, we analytically derive the
order parameter equations associated with nonequilibrium phase transitions in
the thermodynamic limit. Solving them numerically, we systematically
investigate the model parameter dependences of the appearance and disappearance
of synchronization phenomena. Demonstrating bifurcations from chaotic
attractors in the deterministic limit to limit cycle attractors with increasing
noise intensity, we confirm the occurrence of nonequilibrium phase transitions
including inter-cluster synchronization induced by external white Gaussian
noise.
