Trichotomous noise induced resonance behavior of two coupled harmonic oscillators with fluctuating mass

Abstract

This paper investigates the stochastic resonance phenomenon in two coupled harmonic oscillators with fluctuating mass. The fluctuation of the mass is modeled as a trichotomous noise. Applying the Shapiro-Loginov formula and the Laplace transform, the statistic synchronization between the two particles is obtained and defined. Then, the analytical expression of the output amplitude gain is derived. Based on the analytical result, the influence of the trichotomous noise’steady-state probability and the coupling strength on the resonance behaviors of the output amplitude gain are discussed. In the strong noise region, the output amplitude gain of the system will exhibit stochastic resonance with change of the steady state probability, so that the system output amplitude gain induced by trichotomous noise is greater than induced by dichotomous noise. Beside, the system output amplitude gain has resonance behavior with respect to the coupling strength too. Unlike the case of dichotomous noise, the system’s output amplitude gain can show double-peaks resonance when driven by trichotomous noise.

A coupled fractional-order system with fluctuating frequency and its application in bearing fault diagnosis

“…For example, SR has been observed in fractional-order systems subject to random mass fluctuation and random frequency fluctuation [17][18][19][20][21]. Since many systems are coupled by particles while the above studies only consider a single particle, neglecting the interaction between particles, then the resonant behaviors of coupled fractional systems were studied [22][23][24][25][26][27][28]. Peng et al studied the resonant behaviors of two coupled harmonic oscillators with mass fluctuation modelled by trichotomous noise, and found that the output amplitude gain of the system is related to the coupling strength and the system reaches its optimum when it is coupled [22].…”

“…Since many systems are coupled by particles while the above studies only consider a single particle, neglecting the interaction between particles, then the resonant behaviors of coupled fractional systems were studied [22][23][24][25][26][27][28]. Peng et al studied the resonant behaviors of two coupled harmonic oscillators with mass fluctuation modelled by trichotomous noise, and found that the output amplitude gain of the system is related to the coupling strength and the system reaches its optimum when it is coupled [22]. Yu et al investigated the resonance of two coupled integer and fractional harmonic oscillators with fluctuating mass modelled by dichotomous noise, and showed that the coupling strength triggers three types of resonance behavior: parameter-induced SR, bona-fide resonance, and SR [23,24].…”

Adaptive Modulation Stochastic Resonance of Two-Dimensional Asymmetric Bistable System and its Application in Bearing Fault Diagnosis

“…The linear coupled stochastic resonance under different noises (e.g. levy noise, trichotomous noise) was investigated in the references [13][14][15][16], and the results showed that the linear coupled system had better performance compared with the conventional single bistable system and Duffing oscillator system, and also had good detection effect on the actual bearing fault diagnosis signal. Reference [17] proposed a novel adaptive stochastic resonance method based on coupled bistable systems, which compared with the cascaded bistable stochastic resonance system and suggested that coupled bistable SR system can enhance the target signal while suppressing the low-frequency and highfrequency interferences, whose output behavior exhibited good bandpass filtering characteristic.…”