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

Liu, Lin; Chen, Cong; Zhong, Shun; Wang, Huiqi

doi:10.1007/s10955-015-1265-2

Cited by 16 publications

(3 citation statements)

References 39 publications

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“…As a generalization of the classical harmonic oscillator, the fractional oscillator (FO) plays a significant role, and the characteristics of fractional operators makes them suitable for describing those systems with long-range dependence and long memory. Therefore, close attention has been paid to exploring SR mechanics in fractional noisy oscillators including frequency fluctuation in more recent years [40][41][42][43][44][45]. For example, Soika et al [42] investigated the resonant behavior of a fractional oscillator with fluctuating frequency, and discussed the necessary and sucient conditions for the cooperation eects arising as a consequence of the interplay of colored noise and memory.…”

Section: Introductionmentioning

confidence: 99%

Trichotomous noise induced stochastic resonance in a fractional oscillator with random damping and random frequency

2016

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Several corrections were not applied at the proofreading stage. The Production team regrets the errors, and presents the corrections here. These corrections do not aect the scientific outcomes of the paper.(1) On page 6, there should be a '.' at the end of the last one of the equation (6).(2) On page 6, there should be a '.' at the end of the equation (7).(3) On the 6th row of page 7, there is an extra x˙ in the expression of d 34 .(4) On the 7th row of page 7, ' and x 1 (0), x 2 (0) and x 3 (0) are the initial conditions'.should be corrected into 'and x 1 (0), x 2 (0), x 3 (0), x˙0 1 ( ), x˙0 2 ( ), x˙0 3 ( ) are the initial conditions'.

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Section: Introductionmentioning

confidence: 99%

Trichotomous noise induced stochastic resonance in a fractional oscillator with random damping and random frequency

2016

Self Cite

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“…Therefore, to extend the application of SR, some scholars have studied fractional-order damping systems as alternatives to integer order damping. 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].…”

Section: Introductionmentioning

confidence: 99%

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

He¹,

Liu²,

Jiang³

2023

Phys. Scr.

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In this paper, a coupled fractional-order system with fluctuating frequency driven by different periodic signals under various damping strength is investigated. Firstly, based on the Shapiro-Loginov formula and Laplace transform method, the expressions for the output amplitude gain (OAG) of the two subsystems are derived and the resonant behaviors of particles are analyzed. The OAG exhibits various resonance behaviors in response to variations in system parameters, input signals and dichotomous noise, including parameter-induced stochastic resonance, bona-fide resonance and stochastic resonance. Especially, the average behavior of the two output signals is synchronized when two subsystems’ input signals and damping strengths are equal, which is verified in the numerical simulation. Finally, the proposed system is applied to the bearing fault diagnosis to evaluate its engineering application value. The results prove that the system is effective in diagnosing fault signals and has excellent performance.

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“…On the other hand, as a natural generalization of integral-order stochastic dynamical system, the research of SR based on fractional-order stochastic dynamical system gradually attracted great interest [17][18][19]. In fact, the friction term in the classical Langevin equation is only dependent on the current speed, which is modeled as -γẋ (t).…”

Section: Introductionmentioning

confidence: 99%

Stochastic resonance of fractional-order Langevin equation driven by periodic modulated noise with mass fluctuation

Yang

Deng²,

Ren

2020

Adv Differ Equ

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The stochastic resonance (SR) of a second-order harmonic oscillator subject to mass fluctuation and periodic modulated noise in viscous media is studied. The mass fluctuation noise is modeled as dichotomous noise and the memory of viscous media is characterized by fractional power kernel function. By using the Shapiro-Loginov formula and Laplace transform, we got the analytical expression of the first moment of the steady-state response and studied the relationship between the system response and the system parameters in the long-time limit. The simulation results show the non-monotonic dependence between the response amplitude and the input signal frequency, noise parameters of the system, etc, which indicates that the bona fide resonance and the generalized SR phenomena appear. Furthermore, the mass fluctuation noise, modulation noise, and the fractional order work together, producing more complex dynamic phenomena than the integral-order system. For example, there is a transition from bimodal resonance to unimodal resonance between the amplitude and the driving frequency under different fractional orders.

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

Cited by 16 publications

References 39 publications

Trichotomous noise induced stochastic resonance in a fractional oscillator with random damping and random frequency

Trichotomous noise induced stochastic resonance in a fractional oscillator with random damping and random frequency

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

Stochastic resonance of fractional-order Langevin equation driven by periodic modulated noise with mass fluctuation

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