Search

Due to the interest of anomalous diffusion phenomena and their application, our work has widely studied a fractional-order generalized Langevin Equation (FGLE) with a generalized Mittag–Leffler (GML) noise. Significantly, the spectral of GML noise involving three parameters is well addressed. Furthermore, the spectral amplification (SPA) of an FGLE has also been investigated. The generalized stochastic resonance (GSR) phenomenon for FGLE only influenced by GML noise has been found. Furthermore, material GSR for FGLE influenced by two types of noise has been studied. Moreover, it is found that the GSR behaviors of the FGLE could also be induced by the fractional orders of the FGLE. [ABSTRACT FROM AUTHOR]

Due to the interest of anomalous diffusion phenomena and their application, our work has widely studied a fractional-order generalized Langevin Equation (FGLE) with a generalized Mittag–Leffler (GML) noise. Significantly, the spectral of GML noise involving three parameters is well addressed. Furthermore, the spectral amplification (SPA) of an FGLE has also been investigated. The generalized stochastic resonance (GSR) phenomenon for FGLE only influenced by GML noise has been found. Furthermore, material GSR for FGLE influenced by two types of noise has been studied. Moreover, it is found that the GSR behaviors of the FGLE could also be induced by the fractional orders of the FGLE.

The classical tri-stable stochastic resonance (CTSR) has the weakness of output saturation, which restricts the ability to enhance weak signal detection. To overcome the limitation of output saturation, a piecewise unsaturated multi-stable stochastic resonance (PUMSR) method is proposed. Due to the presence of trichotomous noise in practical application, this paper explores the PUMSR under a trichotomous noise environment. The performance of PUMSR is evaluated by means of an index, mean signal-to-noise ratio increase (MSNRI). In order to meet the adiabatic approximation conditions, the signal is secondary sampled and a genetic algorithm (GA) is implemented to optimize the system parameters. Simulation experiments demonstrate that the proposed PUMSR system is superior to the CTSR system in terms of its ability to extract signals at multi-frequency. The PUMSR is then applied to the diagnosis of bearing faults. It is further proved that the PUMSR system has good performance in bearing fault diagnosis and has great feasibility in real engineering application.

The stochastic resonance (SR) behavior of a trapped particle characterized by a three-dimensional fractional-order stochastic equation with Markovian trichotomous noise has been studied in our work. Significantly, an exact expression of the first moment is derived by Shapiro-Loginov formula. Furthermore, the non-monotonic behavior of output amplitude is further discussed. Moreover, the asymptotic behaviors of relaxation function have been discussed. And the periodicity of the time series of the first moment is also addressed to verify the exact expression of the first moment in a long time. Particularly, the SR phenomenon induced by the trichotomous noise is studied. It is worthy to mention that the existence of SR in a fractional Langevin equation (FLa graphical method. Material resonance behaviors of the output amplitude versus the system parameters and noise parameters are extensively investigated. Especially, reverse SR phenomenon, stochastic multiresonance phenomena and bona fide SR are addressed in detail.

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]

Stochastic resonance (SR) is investigated in an underdamped periodic potential system subject to cosine signal with symmetric trichotomous noise measured by using the average input energy per period ⟨ W ¯ ⟩ numerically. The results show that: (1) The curve of ⟨ W ¯ ⟩ has the peak value as a function of trichotomous noise intensity D in a domain parameter, that is, SR can occur in the system; (2) SR can be enhanced by increasing signal amplitude A , trichotomous noise amplitude a and stationary probability q and can be weakened by increasing asymmetric coefficient α ; and (3) the peak value of ⟨ W ¯ ⟩ first increases and then decreases with the increase in friction coefficient γ . However, the peak value of ⟨ W ¯ ⟩ decreases at first and then increases with the increase in signal frequency ω . [ABSTRACT FROM AUTHOR]

In this paper, stochastic resonance in a fractional oscillator with a power-law friction kernel subject to random damping is investigated both theoretically and numerically. The influence of a fluctuating damping is modeled as multiplicative trichotomous noise. The exact expression of the first moment of the system $$'$$ s steady response has been calculated. It is shown that the interplay between multiplicative trichotomous noise and memory effect leads to stochastic resonance in the proposed system. The output amplitude gain (OAG) shows non-monotonic dependence on the driving frequency of the input signal and the characteristics of the noise. Furthermore, a multiresonance-like behavior of the OAG as function of the driving frequency and the inverse-stochastic resonance behavior of the OAG as function of the noise switching rate are observed, which is previously reported and believed to be absent in the case of the non-memory oscillator. Finally, some numerical simulations are performed to support the theoretical analyses. [ABSTRACT FROM AUTHOR]

This paper studies the phenomenon of stochastic resonance (SR) in a bistable system with time delay driven by trichotomous noise. Firstly, a method of numerical simulation for trichotomous noise is presented and its accuracy is checked using normalized autocorrelation function. Then the effects of feedback strength and time delay on the system responses and signal-to-noise ratio (SNR) are studied. The results show that negative feedback strength is more beneficial than positive to promote SR. The effect of time delay on SR is related to the value of feedback strength. The influence of the signal amplitude and frequency on SR is also investigated. It is found that large amplitude and small frequency of the signal can promote the occurrence of SR. Finally, the influence of the amplitude and stationary probability of trichotomous noise on SNR are discussed. [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]

A one-dimensional overdamped system consisting of a symmetric periodic potential, a constant bias force and a trichotomous noise was investigated. In the frame of master equations, we derived analytical expression of its current. By means of numerical calculations, the results indicate that the current first increases, then decreases and finally increases with the bias force increasing, i.e., an absolute negative mobility (ANM) phenomenon. Our further investigations presented dependence of the ANM phenomenon on parameters of the noise. Its intrinsic physical mechanism was also open up, and a minimal model with ANM phenomenon is demonstrated. [ABSTRACT FROM AUTHOR]

We investigate the stochastic resonance (SR) phenomenon in a fractional oscillator with random mass under the external periodic force. The fluctuations of the mass are modeled as a trichotomous noise. Applying the Shapiro-Loginov formula and the Laplace transform technique, we obtain the exact expression of the first moment of the system. The non-monotonic behaviors of the spectral amplification (SPA) versus the driving frequency indicate that the bona fide SR appears. The necessary and sufficient conditions for the emergence of the generalized stochastic resonance phenomena on the noise flatness and on the noise intensity in the particular case of $$\Omega =\omega _0 ,v\rightarrow 0$$ are established. Particularly, the hypersensitive response of the SPA to the noise intensity is found, which is previously reported and believed to be absent in the case of dichotomous noise. [ABSTRACT FROM AUTHOR]

Abstract: The stochastic resonance (SR) in a second-order linear system driven by a trichotomous noise and an external periodic signal is investigated. By the use of the properties of the trichotomous noise and the Shapiro–Loginov formula, the exact expression for the output spectral amplification (SPA) of the system is obtained. The non-monotonic influence of the coefficient of the trichotomous noise on the SPA is found. It is shown that the SPA is a non-monotonic function of the amplitude, the correlation rate and the probability of the trichotomous noise. The SPA varies non-monotonically with the frequency of the driving signal, the damping coefficient and the frequency of the linear system. [Copyright &y& Elsevier]

In this paper, the phenomenon of stochastic resonance (SR) in a prototype fluctuating damping harmonic oscillator with trichotomous Markovian noise is investigated. The exact expression of output amplitude gain has been calculated using the well-known Shapiro-Loginov formula. The phenomenon of SR has been found in a broad sense-that is, the non-monotonic behavior of output amplitude gain as a function of noise parameters. Then the influences of noise amplitude, noise switching rate, and noise flatness on the output amplitude gain have also been discussed. Finally, the reverse resonance phenomenon has been presented. [ABSTRACT FROM AUTHOR]

Abstract: In addition to the case usually considered of a stochastic harmonic oscillator subject to an external random force (Brownian motion in a parabolic potential) or to a random frequency and random damping, we consider an oscillator with random mass subject to an external periodic force, where the molecules of a surrounding medium, which collide with a Brownian particle are able to adhere to the oscillator for a random time, changing thereby the oscillator mass. The fluctuations of mass are modelled as trichotomous noise. Using the Shapiro–Loginov procedure for splitting the correlators, we found the first two moments. It turns out that the second moment is a non-monotonic function of the characteristics of noise and periodic signal, and for some values of these parameters, the oscillator becomes unstable. [Copyright &y& Elsevier]

We investigate stochastic resonance in an underdamped linear system subjected to multiplicative trichotomous noise. We carry out the Shapiro-Loginov formula to find the exact expression of output amplitude gain, and the impacts of the input signal frequency and noise parameters will be observed, such as noise switching rate or noise correlation time, noise amplitude and noise flatness. Then one can find the stochastic resonance for the proposed linear system. [ABSTRACT FROM AUTHOR]

The influence of noise flatness and memory-time on the dynamics of a generalized Langevin system driven by an internal Mittag-Leffler noise and by a multiplicative trichotomous noise is studied. In the asymptotic limit at a short memory time the dynamics corresponds to a system with a pure power-law memory kernel for a viscoelastic type friction. However, at long and intermediate memory times the behaviour of the system has a qualitative difference. In particular, a critical memory time and a critical memory exponent have been found, which mark dynamical transitions in the resonant behaviour of the system. The obtained results show that the model considered is quite robust and may be of interest also in cell biology. [ABSTRACT FROM AUTHOR]

Recently Ru-Yin Chen et al. (Phys. Lett. A 379 (2015) 2169–2173) presented results on the absolute negative mobility (ANM) in a one-dimensional overdamped system and claimed that a new minimal model of ANM was proposed. We suggest that the authors introduced a mistake in their calculations. Then we perform a precise numerical simulation of the corresponding Langevin equation to show that the ANM phenomenon does not occur in the considered system. [ABSTRACT FROM AUTHOR]

The classical tri-stable stochastic resonance (CTSR) has the weakness of output saturation, which restricts the ability to enhance weak signal detection. To overcome the limitation of output saturation, a piecewise unsaturated multi-stable stochastic resonance (PUMSR) method is proposed. Due to the presence of trichotomous noise in practical application, this paper explores the PUMSR under a trichotomous noise environment. The performance of PUMSR is evaluated by means of an index, mean signal-to-noise ratio increase (MSNRI). In order to meet the adiabatic approximation conditions, the signal is secondary sampled and a genetic algorithm (GA) is implemented to optimize the system parameters. Simulation experiments demonstrate that the proposed PUMSR system is superior to the CTSR system in terms of its ability to extract signals at multi-frequency. The PUMSR is then applied to the diagnosis of bearing faults. It is further proved that the PUMSR system has good performance in bearing fault diagnosis and has great feasibility in real engineering application. [ABSTRACT FROM AUTHOR]

• The first moment of a three-dimensional fractional-order stochastic equation is derived. • The asymptotic behaviors of relaxation function have been discussed. • The periodicity of the time series of the first moment is addressed. • Material resonance behaviors of the output amplitude are addressed. The stochastic resonance (SR) behavior of a trapped particle characterized by a three-dimensional fractional-order stochastic equation with Markovian trichotomous noise has been studied in our work. Significantly, an exact expression of the first moment is derived by Shapiro-Loginov formula. Furthermore, the non-monotonic behavior of output amplitude is further discussed. Moreover, the asymptotic behaviors of relaxation function have been discussed. And the periodicity of the time series of the first moment is also addressed to verify the exact expression of the first moment in a long time. Particularly, the SR phenomenon induced by the trichotomous noise is studied. It is worthy to mention that the existence of SR in a fractional Langevin equation (FLa graphical method. Material resonance behaviors of the output amplitude versus the system parameters and noise parameters are extensively investigated. Especially, reverse SR phenomenon, stochastic multiresonance phenomena and bona fide SR are addressed in detail. [ABSTRACT FROM AUTHOR]