Erratum: Trichotomous noise induced stochastic resonance in a fractional oscillator with random damping and random frequency (2016J. Stat. Mech. 023201)

2016 ◽  
Vol 2016 (6) ◽  
pp. 069901
Author(s):  
Li-Feng Lin ◽  
Cong Chen ◽  
Hui-Qi Wang
Keyword(s):  
Stochastic Resonance ◽  
Fractional Oscillator ◽  
Trichotomous Noise ◽  
Random Frequency

Stochastic resonance for a fractional oscillator with random trichotomous mass and random trichotomous frequency

2017 ◽  
Vol 31 (30) ◽  
pp. 1750231 ◽  
Author(s):  
Lifeng Lin ◽  
Huiqi Wang ◽  
Suchuan Zhong
Keyword(s):  
Stochastic Resonance ◽  
Exact Expression ◽  
Order Moment ◽  
Periodic Signal ◽  
Transformation Technique ◽  
First Order ◽  
Fractional Oscillator ◽  
Trichotomous Noise ◽  
Output Amplitude ◽  
Fractional System

The stochastic resonance (SR) phenomena of a linear fractional oscillator with random trichotomous mass and random trichotomous frequency are investigate in this paper. By using the Shapiro–Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is derived. The numerical results demonstrate that the evolution of the output amplitude is nonmonotonic with frequency of the periodic signal, noise parameters and fractional order. The generalized SR (GSR) phenomena, including single GSR (SGSR) and doubly GSR (DGSR), and trebly GSR (TGSR), are detected in this fractional system. Then, the GSR regions in the [Formula: see text] plane are determined through numerical calculations. In addition, the interaction effect of the multiplicative trichotomous noise and memory can diversify the stochastic multiresonance (SMR) phenomena, and induce reverse-resonance phenomena.

Stochastic Resonance in a Fractional Oscillator with Random Mass and Random Frequency

2015 ◽  
Vol 160 (2) ◽  
pp. 497-511 ◽  
Author(s):  
Li-Feng Lin ◽  
Cong Chen ◽  
Su-Chuan Zhong ◽  
Hui-Qi Wang
Keyword(s):  
Stochastic Resonance ◽  
Random Mass ◽  
Fractional Oscillator ◽  
Random Frequency

Stochastic Resonance in Strongly Coupled Duffing and Van der pol Oscillators Under Trichotomous Noise and Bearing Fault Diagnosis

2019 ◽  
Vol 19 (03) ◽  
pp. 2050023
Author(s):  
Gang Zhang ◽  
Xia Wu ◽  
Tianqi Zhang
Keyword(s):  
Stochastic Resonance ◽  
Coupling Coefficient ◽  
Damping Coefficient ◽  
System Response ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
Strongly Coupled ◽  
Force Coupling ◽  
Trichotomous Noise

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.

Generalized stochastic resonance for a fractional harmonic oscillator with bias-signal-modulated trichotomous noise

2018 ◽  
Vol 32 (07) ◽  
pp. 1850072 ◽  
Author(s):  
Lifeng Lin ◽  
Huiqi Wang ◽  
Xipei Huang ◽  
Yongxian Wen
Keyword(s):  
Stochastic Resonance ◽  
Exact Expression ◽  
Order Moment ◽  
Periodic Signal ◽  
External Excitation ◽  
First Order ◽  
Trichotomous Noise ◽  
Output Amplitude ◽  
Fractional Harmonic Oscillator ◽  
Amplitude Amplification

For a fractional linear oscillator subjected to both parametric excitation of trichotomous noise and external excitation of bias-signal-modulated trichotomous noise, the generalized stochastic resonance (GSR) phenomena are investigated in this paper in case the noises are cross-correlative. First, the generalized Shapiro–Loginov formula and generalized fractional Shapiro–Loginov formula are derived. Then, by using the generalized (fractional) Shapiro–Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is obtained. The numerical results show that the evolution of the output amplitude amplification is nonmonotonic with the frequency of periodic signal, the noise parameters, and the fractional order. The GSR phenomena, including single-peak GSR, double-peak GSR and triple-peak GSR, are observed in this system. In addition, the interplay of the multiplicative trichotomous noise, bias-signal-modulated trichotomous noise and memory can induce and diversify the stochastic multi-resonance (SMR) phenomena, and the two kinds of trichotomous noises play opposite roles on the GSR.

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