Nonlinear noise-induced transitions in active rotator model

We investigate noise-induced transitions in active rotator model with a fluctuating threshold in the presence of an additive noise. The fluctuation of the threshold depends on the additive noise in a nonlinear fashion. In the white-noise limit of the fluctuation, the Fokker-Planck equation of the system reduces to that of the system with correlated linear fluctuation implying that the nonlinearity may be transformed into the correlation of linear noises. We also investigate the system with a nonlinear colored noise which depends on the additive noise as its square. The system shows a single peak, hive peaks, and three peaks in its steady state probability distribution according to the noise intensities and the correlation time whose change leads to peak-creating, peak-splitting, and peak-merging transitions.