Unsaturated piecewise bistable stochastic resonance with three kinds of asymmetries driven by multiplicative and additive noise

Abstract

The performance of an unsaturated piecewise bistable stochastic resonance (UPBSR) with three kinds of asymmetries driven by multiplicative and additive Gaussian white noise 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 deriving the output signal-to-noise ratio (SNR), the behavior of asymmetric UPBSR under two independent noises and correlated noises is analyzed. Enhancement ability and noise immunity are adopted as SR evaluation index. Moreover, the mean first passage time (MFPT), is adopted to discuss the transient properties of UPBSR system. Finally, for SNR analysis, the results show that asymmetric SR outperforms symmetric SR when the asymmetric factor is in the appropriate range, and the BDWA dominates the three cases. When subject to two independent noises, multiplicative noises always shows a suppression on SR. However, when the two noises are correlated, the effect of each parameter on SNR becomes complicated, the same parameter may have the exact opposite effect on SNR in different situations. In addition, the correlation intensity λ play an important role in SR. It can excite SR to appear as a double peak, which is different from the conventional SR. Despite the effects of individual parameters on SNR are highly coupled, the introduction of three kinds of asymmetries and correlated noise can improve the performance of SR. As for MFPT analysis, when driven by independent multiplicative and additive noise, MFPT exhibits similar monotonically decreasing behavior in various cases. However, the noise-enhanced stability (NES) phenomenon is excited when driven by the correlated multiplicative and additive noise. In the case of WDA and BDWA, both appropriate λ and noise intensity ratio R favor the NES phenomenon, while in the case of WWA, the NES phenomenon is suppressed.