Unsaturated piecewise bistable stochastic resonance with three kinds of asymmetries and time-delayed feedback. (August 2022) - Ma, Tianchi; Song, Di; Shen, Junxian; Xu, Feiyun
Abstract: The performance of an unsaturated piecewise bistable stochastic resonance (UPBSR) with three kinds of asymmetries and time-delayed feedback is investigated. Firstly, by introducing an asymmetric factor into UPBSR potential, three kinds of asymmetries are constructed, i.e., well-depth asymmetry (WDA), well-width asymmetry (WWA), and both well-depth and well-width asymmetry (BDWA). Then, by using two-state theory and small delay approximation, the output signal-to-noise ratio (SNR) is derived to analyze the behavior of SR. Enhancement ability and noise immunity are adopted as SR evaluation index. Moreover, as an intermediate result in the calculation of the SNR, the mean first passage time (MFPT), is often used to discuss the transient properties of nonlinear systems. Finally, for SNR analysis, the results show that asymmetric SR outperforms symmetric SR when the asymmetric factor is in the appropriate range, and the WDA dominates the three cases. In addition, the effect of feedback intensity on SR depends heavily on the asymmetric cases, it plays the opposite role in different asymmetric cases. In contrast, the effect of time delay is independent on the asymmetric cases, which always exhibits an improvement of SR noise immunity. As for MFPT analysis, the small γ and β are conducive to the transition of the particles between potential wells, while τ almost has no effect on the transition of particles. Highlights: UPBSR with three kinds of asymmetries and time-delayed feedback is studied. Well-depth asymmetry dominates the three kinds of asymmetries. The effect of feedback intensity on SR depends heavily on the asymmetric cases. Time delay always exhibits an improvement of SR noise immunity.