Bifurcation phenomena of mean-field coupled self-sustained oscillators with two different time scales under the influence of external white noise

We report stochastic phenomena of inter-cluster synchronization in ensembles of coupled self-sustained oscillators with different time scales. A mean-field model of two interconnected clusters of coupled limit cycle oscillators having same trajectories with two native frequencies is considered to analytically derive the time evolution of the order parameters in the thermodynamic limit. A set of the order parameters obtained for the system exhibits noise induced bifurcations, including those from torus type attractors to fixed point ones for the case with two different heat baths in accordance with the introduction of the time scale.