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Weak signal detection is an important topic, which has been widely studied in various fields. Different from other signal processing methods, stochastic resonance (SR) can utilize noise to enhance the characteristic frequency. Inspired by the unique advantage of SR, the strongly coupled Duffing and Van der pol SR system (SCD-VSR) is investigated. The simulation results show that the relationship between the output average signal–noise ratio increase (MSNRI) and different jump values of trichotomous noise presents different odd symmetrical distribution. It is also found that a double SR phenomenon could be observed when the damping coefficient of Van der pol system is small. Moreover, as the damping coefficient of the Duffing system increases, the output response would become gradually smooth. In addition,a smaller damping force coupling coefficient combined with a large restoring force coupling coefficient would achieve better system response. In the case of detecting an analog signal, MSNRI of SCD-VSR is larger than that of both classical bistable SR system (CBSR) and coupled Duffing SR system (CDSR). In addition, the experiments suggest that SCD-VSR could obtain a higher MSNRI and better detection effect, which implies the performance is superior to CBSR and CDSR. [ABSTRACT FROM AUTHOR]

The classical bistable stochastic resonance (CBSR) has the disadvantage of output saturation, which limits the enhancement capability for weak signal detection. To break the limitation of output saturation, a novel unsaturated piecewise non-linear bistable stochastic resonance (PNBSR) method is proposed. Because the trichotomous noise exists in practical engineering, the PNBSR under trichotomous noise is explored in this paper. The performance of PNBSR is evaluated by the index, i.e., the mean of M times signal-to-noise ratio increase (MSNRI). The double-peak phenomenon of SR is observed under trichotomous noise. Experiments reveal that the proposed PNBSR method performs best on extracting characteristic components from a strong noise background, compared with the CBSR method and the traditional digital filter. Then, the PNBSR is applied to the fault diagnosis of rolling element bearings. The paper focuses on solving practical engineering problems with mathematical methods. [ABSTRACT FROM AUTHOR]

The stability analysis of a Beddington-DeAngelis (B-D) type predator-prey model driven by symmetric trichotomous noises is presented in this paper. Using the Shapiro-Loginov formula, the first-order and second-order solution moments of the system are obtained. The moment stability conditions of the B-D predator-prey model are given by using Routh-Hurwitz criterion. It is found that the stabilities of the first-order and second-order solution moments depend on the noise intensities and correlation time of noise. The first-order and second-order moments are stable when the correlation time of noise is increased. That is, the trichotomous noise plays a constructive role in stabilizing the solution moment with regard to Gaussian white noise. Finally, some numerical results are performed to support the theoretical analyses. [ABSTRACT FROM AUTHOR]