Stochastic resonance in a delayed triple-well potential driven by correlated noises

Dynamical analysis and fault detection application of a time-delayed multi-stable stochastic resonance system driven by white correlated noises

Bearing fault diagnosis is a crucial means to ensure the normal operation of machinery, reduce maintenance costs, enhance equipments safety and extend the service life of bearings. However, the noise interference in input signals often affects the effective extraction of bearing fault signals. In this paper, a time-delay multi-stable stochastic resonance (SR) system driven by white correlated noises is proposed. Firstly, the expressions of the steady-state probability density (SPD) function and the mean first passage time (MFPT) is derived. Simultaneously, we delve into the influences of various system parameters, including multiplicative noise intensity, additive noise intensity, noise correlated strength, time-delay, and time-delay feedback intensity, on the dynamical behavior exhibited by particles within the system. Then, according to the signal-to-noise ratio (SNR) formula, the paper investigates the impact of system parameters on the SNR. It is found that the ease of SR occurrence is directly related to the system parameters. Finally, the experimental results demonstrate that the proposed method exhibits superior performance in detecting faults compared with the classical bistable SR system and the quad-stable SR system.

Characterizing stochastic resonance in a triple cavity

Many biological systems possess confined structures, which produce novel influences on the dynamics. Here, stochastic resonance (SR) in a triple cavity that consists of three units and is subjected to noise, periodic force and vertical constance force is studied, by calculating the spectral amplification η numerically. Meanwhile, SR in the given triple cavity and differences from other structures are explored. First, it is found that the cavity parameters can eliminate or regulate the maximum of η and the noise intensity that induces this maximum. Second, compared to a double cavity with similar maximum/minimum widths and distances between two maximum widths as the triple cavity, η in the triple one shows a larger maximum. Next, the conversion of the natural boundary in the pure potential to the reflection boundary in the triple cavity will create the necessity of a vertical force to induce SR and lead to a decrease in the maximum of η. In addition, η monotonically decreases with the increase of the vertical force and frequency of the periodic force, while it presents several trends when increasing the periodic force's amplitude for different noise intensities. Finally, our studies are extended to the impact of fractional Gaussian noise excitations. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Stochastic resonance and bifurcations in a harmonically driven tri-stable potential with colored noise

Stochastic resonance (SR) and stochastic bifurcations are investigated numerically in a nonlinear tri-stable system driven by colored noise and a harmonic excitation. The power spectral density, signal-to-noise ratio, stationary probability density (SPD), and largest Lyapunov exponent (LLE) are calculated to quantify SR, P-bifurcation, and D-bifurcation, respectively. The effects of system parameters, such as noise intensity and correlation time, well-depth ratio, and damping coefficient, on SR and stochastic bifurcations are explored. Numerical results show that both noise-induced suppression and SR can be observed in this system. The SPD changes from bimodal to trimodal and then to the unimodal structure by choosing well-depth ratio, correlation time, and noise intensity as bifurcation parameters, which shows the occurrence of stochastic P-bifurcation. The stochastic D-bifurcation is found through the calculation of LLE. Moreover, the relationship between SR and stochastic bifurcation is explored thoroughly. It indicates that the optimal SR occurs near D-bifurcation and can be realized with weak chaos by adjusting the proper parameters. Finally, the tri-stable energy harvester is chosen as an example to show the improvement of the system performance by exploiting SR and stochastic bifurcations.