Noise-intensity fluctuation in Langevin model and its higher-order Fokker-Planck equation

► We investigate a Langevin model with temporal fluctuations in noise intensity. ► A higher-order Fokker-Planck equation (HFPE) of the system is derived. ► Stationary distributions of the HFPE are calculated in three typical cases. ► The existence of noise-intensity fluctuations induces a bimodal-to-trimodal transition.