Rotational stochastic resonance in multistable systems

Stochastic resonance is a well-known phenomenon that intermediate amount of noise can enhance the signal-to-noise ratio of systems subjected to weak signals. Since the discovery of stochastic resonance, it has aroused tremendous attention during the past several decades due to its counterintuitive nature. Previous focus is mainly devoted to low-dimensional bistable systems with only one sinusoid-type weak signal. In this work, we extend the boundary of the traditional stochastic resonance by considering two-dimensional multistable systems driven by rotational sinusoid-type weak signals. We consider an artificial triple-well system and also a more realistic four-well system model. The rotational characteristics of noise-induced switching between stable wells (clockwise or anticlockwise) can be controlled by the signal frequency and the noise intensity, which is a markedly difference from the classical ones. Thus, we term it as rotational stochastic resonance. The rotational stochastic resonance phenomenon can be illustrated by the Penrose stairs and can be quantified by the proposed minimum potential coincidence index and the minimum potential locking index. The rotational stochastic resonance and its control investigated in this paper may shed some light on more complex resonance phenomena and experimental applications.