Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system

Yang, Jianhua; Sanjuán, Miguel A. F.; Liu, Houguang; Litak, Grzegorz; Li, Xing

doi:10.1016/j.cnsns.2016.05.001

Cited by 82 publications

(19 citation statements)

References 33 publications

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“…Since the response mechanism of nonlinear systems are very complex [42,44,47], in order to verify the aforementioned theoretical results, the parameters of equations (6) and 7are chosen as θ � 0.5, g � 1.0, λ � 1.0, ω � 1.0, and c � 0.1. Figure 3 shows the variations of the largest Lyapunov exponent determined by equation (27).…”

Section: Trivial Solutions and Their Stabilitymentioning

confidence: 99%

Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow‐Band Stochastic Parametric Excitations

2019

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To improve energy harvesting performance, this paper investigates the resonance mechanism of nonlinear vibrational multistable energy harvesters under narrow-band stochastic parametric excitations. Based on the method of multiple scales, the largest Lyapunov exponent which determines the stability of the trivial steady-state solutions is derived. The first kind modified Bessel function is utilized to derive the solutions of the responses of multistable energy harvesters. Then, the first-order and second-order nontrivial steady-state moments of multistable energy harvesters are considered. To explore the stochastic bifurcation phenomenon between the nontrivial and trivial steady-state solutions, the Fokker–Planck–Kolmogorov equation corresponding to the two-dimensional Itô stochastic differential equations is solved by using the finite difference method. In addition, the mechanism of the stochastic bifurcation of multistable energy harvesters is analyzed for revealing their unique dynamic response characteristics.

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Section: Trivial Solutions and Their Stabilitymentioning

confidence: 99%

Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow‐Band Stochastic Parametric Excitations

2019

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“…It means that FrSR has the typical stochastic P-bifurcation behavior when the fractional-order α is near 1. 24 Due to the effect of driving signal, the stochastic P-bifurcation behavior disappears when the fractional-order α is large.…”

Section: Effect Of Fractional-order αmentioning

confidence: 99%

Effect of scale-varying fractional-order stochastic resonance by simulation and its application in bearing diagnosis

Chi

Kang

Zhang

et al. 2019

Int. J. Model. Simul. Sci. Comput.

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Bearing is among the most widely used components in rotating machinery. Its failure can cause serious economic losses or even disasters. However, the fault-induced impulses are weak especially for the early failure. As to the bearing fault diagnosis, a novel bearing diagnosis method based on scale-varying fractional-order stochastic resonance (SFrSR) is proposed. Signal-to-noise ratio of the SFrSR output is regarded as the criterion for evaluating the stochastic resonance (SR) output. In the proposed method, by selecting the proper parameters (integration step [Formula: see text], amplitude gain [Formula: see text] and fractional-order [Formula: see text]) of SFrSR, the weak fault-induced impulses, the noise and the potential can be matched with each other. An optimal fractional-order dynamic system can be generated. To verify the proposed SFrSR, numerical tests and application verification are conducted in comparison with the traditional scale-varying first-order SR (SFiSR). The results prove that the parameters [Formula: see text] and [Formula: see text] affect the SFrSR effect seriously and the proposed SFrSR can enhance the weak signal while suppressing the noise. The SFrSR is more effective for bearing fault diagnosis than SFiSR.

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“…Fractional time derivative d n B/dt n can be added in our lump model thanks to Grunwald-Letnikov or Riemman-Liouville definitions [21][22][23][24][25]. Both of them are particular cases of a general fractional order operator namely, the first one represents the n order derivative, while the other represents the n fold integral.…”

Section: Fractional Modelmentioning

confidence: 99%

Fractional model of magnetic field penetration into a toroidal soft ferromagnetic sample

Ducharne

Sebald

Guyomar

et al. 2017

Int. J. Dynam. Control

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We propose an original approach to solve the coupled problem of alternative magnetic field penetration inside a toroidal soft ferromagnetic sample and frequency dependent magnetic hysteresis. Local repartition of ferromagnetic losses depends on the instantaneous material properties and on the frequency of the excitation field waveform. A correct solution to the model, with respect to this repartition, implies a higher resolution in two dimensions of the diffusion equation including local dynamic hysteresis consideration. The resulting model gives precious local information but requires complex parameter setting, high computational capacity and long simulation time. Due to the toroidal shape, a single dimension algorithm solving of the diffusion equation is clearly insufficient and it would lead to inaccurate simulation results. Consequently, a large number of discretization nodes and extended simulation time must be considered in two dimensional configurations. In our alternative solution, starting from a lumped model, we add a fractional time derivative of the dynamic hysteresis losses. It leads to an accurate formulation of the problem with a reduction in complexity and simulation times.

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Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system

Cited by 82 publications

References 33 publications

Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow‐Band Stochastic Parametric Excitations

Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow‐Band Stochastic Parametric Excitations

Effect of scale-varying fractional-order stochastic resonance by simulation and its application in bearing diagnosis

Fractional model of magnetic field penetration into a toroidal soft ferromagnetic sample

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