Output Amplitude Gain Research Articles

Stochastic resonance in a fractional oscillator subjected to multiplicative trichotomous noise

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.

Mittag-Leffler noise induced stochastic resonance in a generalized Langevin equation with random inherent frequency

The generalized stochastic resonance (GSR) and the bona fide stochastic resonance (SR) in a generalized Langevin equation driven by a periodic signal, multiplicative noise and Mittag-Leffler noise are extensively investigated. The expression of the frequency spectrum of the Mittag-Leffler noise is studied. Using the Shapiro–Loginov formula and Laplace transformation technique, the exact expressions of the output amplitude gain and the signal-to-noise ratio are obtained. The simulation results turn out that the output amplitude gain and the signal-to-noise ratio are non-monotonic functions of the characteristics of noise parameters and system parameters. Especially, the influence of the memory exponent and memory time of Mittag-Leffler noise could induce the GSR phenomenon. The influence of the driving frequency could induce the bona fide stochastic resonance. It is found that the system with fractional memory exponent could be more easily induced SR phenomenon than the system with integer memory exponent.

Nonlinear effect of time delay on the generalized stochastic resonance in a fractional oscillator with multiplicative polynomial noise

We investigate generalized stochastic resonance (GSR) in a fractional harmonic oscillator with time delay and fluctuation damping. Considering that nonlinear noise widely exists in actual systems compared with linear noise, the fluctuation of damping is modeled as polynomial trichotomous noise. The analytical expression of the output amplitude gain is derived by applying small delay approximation and stochastic averaging. Simulation results show that the output amplitude gain curves, as functions of time delay versus noise parameters, behave non-monotonically and exhibit typical GSR. Furthermore, nonlinear phenomena of stochastic multi-resonance with two, three, and four peaks are observed. Finally, we provide the phase diagrams for GSR versus time delay with different system parameters. Furthermore, the mechanism underlying the stochastic multi-resonance with two, three, and four peaks, as well as their connections, is elucidated. This study could serve as a theoretical basis for the practical use and control of GSR in future works.

Stochastic resonance for a linear oscillator with two kinds of fractional derivatives and random frequency

The stochastic resonance (SR) behavior for a linear oscillator with two kinds of fractional derivatives and random frequency is investigated. Based on linear system theory, and applying with the definition of the Gamma function and fractional derivatives, we derive the expression for the output amplitude gain (OAG). A stochastic multiresonance is found on the OAG curve versus the first kind of fractional derivative exponent. The SR occurs on the OAG as a function of the second kind of fractional exponent, as a function of the viscous damping and the friction coefficients, and as a function of the system’s frequency. The bona fide SR also takes place on the OAG curve versus the driving frequency.

Stochastic resonance for a fractional linear oscillator with two-kinds of fractional-order derivatives subject to multiplicative and signal-modulated noise

The stochastic resonance phenomenon for a fractional linear oscillator with two-kinds of fractional-order derivatives driven by multiplicative noise and signal-modulated noise is investigated. Based on linear system theory, applying the characteristics of the Gamma function and the definition of the fractional-order derivative, the output-amplitude-gain (OAG) for the oscillator is derived. The analysis results show that the OAG is a non-monotonic function of the exponents of the fractional-order derivatives, the effect of the two exponents on the OAG is different. The OAG varies non-monotonically with a variation of the system driving frequency. The OAG behaves non-monotonically with an increase of the two friction coefficients of the fractional oscillator. The nonlinear dependence of the system frequency and the correlation rate of the multiplicative noise are analyzed.

Resonant behavior of a harmonic oscillator with fluctuating mass driven by a Mittag-Leffler noise

The resonant behavior of a generalized Langevin equation (GLE) in the presence of a Mittag-Leffler noise is studied analytically in this paper. Considering that a GLE with a Mittag-Leffler friction kernel is very useful for modeling anomalous diffusion processes with long-memory and long-range dependence, and the surrounding molecules do not only collide with the Brownian particle but also adhere to the Brownian particle for random time. Thus, we consider the Brownian particle with fluctuating mass, and the fluctuations of the mass are modelled as a dichotomous noise. Applying the stochastic averaging method, we obtain the exact expression of the output amplitude gain of the system. By studying the impact of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude gain. The results indicate that the bona fide SR, the wide sense SR and the conventional SR phenomena occur in the proposed harmonic oscillator with fluctuating mass driven by Mittag-Leffler noise. It is found that when we consider the output amplitude gain versus the driving frequency, the phenomena of stochastic multi-resonance (SMR) with two, three and four peaks are observed, and the quadruple-peaks SR phenomenon had never been observed in previous literature. Besides, when we investigate the dependence of output amplitude gain on the memory exponent, the inverse stochastic resonance (ISR) phenomenon takes place, in contrast to the well-known phenomenon of stochastic resonance. Furthermore, we compare the corresponding ordinary harmonic oscillator without memory to our generalized model, and found that the properties of long-memory and long-range dependence endows our generalized model with more abundant dynamic behaviors than the ordinary harmonic oscillator without memory.

Stochastic resonance in a fractional harmonic oscillator subject to random mass and signal-modulated noise

Stochastic resonance in a fractional harmonic oscillator with random mass and signal-modulated noise is investigated. Applying linear system theory and the characteristics of the noises, the analysis expression of the mean output-amplitude-gain (OAG) is obtained. It is shown that the OAG varies non-monotonically with the increase of the intensity of the multiplicative dichotomous noise, with the increase of the frequency of the driving force, as well as with the increase of the system frequency. In addition, the OAG is a non-monotonic function of the system friction coefficient, as a function of the viscous damping coefficient, as a function of the fractional exponent.

Stochastic resonance in a fractional linear oscillator subject to random viscous damping and signal-modulated noise

The stochastic resonance in a fractional linear system with random viscous damping driven by a dichotomous noise and signal-modulated noise is investigated. By the use of the properties of the noises and the Shapiro-Loginov formula and Laplace transform technology, the exact expression for the mean output-amplitude-gain (OAG) of the system is obtained. The non-monotonic influence of the viscous damping of the oscillator on the OAG is found. It is shown that the OAG is a non-monotonic function of the intensity and the correlation rate of the dichotomous noise. The OAG varies non-monotonically with the friction coefficient, with the frequency of the driving signal, with the frequency of the linear oscillator, as well as with the fractional exponent of the fractional oscillator.

Stochastic resonance in a harmonic oscillator with damping trichotomous noise

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.

Trichotomous noise induced stochastic resonance in a linear system

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.