Phase Noise Induced Characteristic Dynamical Behaviors in a Bistable System

In the past, investigators mainly focused on statistical properties of the stochastic systems subjected to additive or multiplicative Gaussian white noise. In fact, a variety of stochastic systems subjected to phase noise exist commonly in oscillators, phase-locked loops, and periodic force systems. Here characteristic dynamical behaviors of a bistable system subjected to the phase noise are theoretically investigated. The Fokker-Planck equation (FPE) for the stochastic bistable system is analytically derived by means of stochastic dynamical theories. In the basis of the FPE, it is found that: (i) The phase noise can bring about both positive and negative diffusions for the system, depending on intensity of the phase noise. (ii) The phase noise can induce abundant interesting phenomena in the system, such as state transition from bistability to multiple steady states, non-monotonic behavior of variance with the noise intensity, and resonance activation. These research results will not only have an implication for understanding further dynamical behaviors of the systems subjected to the phase noise but also provide an important measure for investigating analytically statistical properties of the stochastic systems.