Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback*

Abstract

Based on adiabatic approximation theory, in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise. The analytical expressions of the mean first-passage time (MFPT) and output signal-to-noise ratio (SNR) are derived by using a path integral approach, unified colored-noise approximation (UCNA), and small delay approximation. The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed. Moreover, three types of asymmetric potential function characteristics are thoroughly discussed. And they are well-depth asymmetry (DASR), well-width asymmetry (WASR), and synchronous action of well-depth and well-width asymmetry (DWASR), respectively. The conclusion of this paper is that the time-delayed feedback can suppress SR, however, the non-Gaussian noise deviation parameter has the opposite effect. Moreover, the correlation time plays a significant role in improving SNR, and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance. Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance, in which no matter whether these signals have low frequency or high frequency, accompanied by strong or weak noise.

Particle Swarm Optimization-Based Variable Scale Asymmetric Stochastic Resonance Bearing Diagnostic Method

“…Empirical investigations and theoretical inquiries alike have elucidated that stochastic resonance architectures imbued with asymmetrical configurations manifest augmented efficacy in discerning weak signals. In the annals of scholarly contributions, Shi [8] delineated an innovative framework of asymmetrical stochastic resonance, integrating temporal feedback mechanisms. Under the perturbation of chromatic noise regimes, the adaptative modulation of the structural parameters engenders pronounced detection advantages vis-à -vis conventional stochastic resonance methodologies.…”

Weak signal detection method based on novel composite multistable stochastic resonance

“…It uses the potential function of a nonlinear system to convert part of the noise energy into useful signal energy, thus using the noise to enhance detection of weak signals. [16,17] At the same time, the SR method can realize weak signal detection by applying noise or adjusting system parameters. Therefore, SR has been developed rapidly and has achieved many achievements.…”

Dynamic responses of an energy harvesting system based on piezoelectric and electromagnetic mechanisms under colored noise

“…By utilizing the implicit harmonic balance method and the Gaussian closure method, Zhu et al [22] discussed the periodic response of a Duffing oscillator under harmonic and random combined excitation. Shi et al [23] studied an asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise. Lin et al [24] invesigated the bursting oscillation and energy harvesting efficiency of a piezoelectric energy harvester in rotational motion under low-frequency excitation.…”