Effects of the colored noise on the resonance at the subharmonic frequency in bistable systems

We investigate the colored noise induced resonance at the 1/3 subharmonic frequency in the overdamped and the underdamped bistable systems by numerical simulations. We find that the resonance at the 1/3 subharmonic frequency may be stronger than the traditional stochastic resonance that occurring at the excitation frequency in some cases. Moreover, we study the effects of the correlation time of the colored noises on the response in detail. If the colored noise is generated by the Ornstein-Uhlenbeck process, there are two major results discovered. Firstly, the critical noise intensity which induces the strongest resonance will increase with the increase of the correlation time. Secondly, when the noise intensity is large enough, the response amplitude at the considered frequency will also increase with the increase of the correlation time. If the colored noise is generated by the power-limited process, the corresponding results are contrary to those in the system under the colored noise excitation that is generated by the Ornstein-Uhlenbeck process. The results in this paper indicate that the type of the colored noise has important effects on the responses of the system.