Stochastic Multi-resonance Phenomena Research Articles

Resonance behavior for a trapped particle described by a three-dimensional fractional Langevin equation

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.

Resonance behavior for an underdamped bistable system driven by square-wave signal and multiplicative noise

The stochastic resonance (SR) behavior for an underdamped bistable system driven by square-wave signal and multiplicative noise is investigated. Under the adiabatic approximation condition, the expression for the system output signal-to-noise ratio (SNR) is obtained. The analysis results show that stochastic multi-resonance phenomenon occurs when the SNR varies with the intensities of the multiplicative and additive noise. SR phenomenon can be observed on the curves of the SNR versus the system bias, versus the amplitude of the dichotomous noise and versus the amplitude of the square-wave signal. Moreover, the SNR varies non-monotonously with the variety of other system parameters.

Noise-induced dynamics in a Josephson junction driven by trichotomous noises

Abstract Noise-induced dynamics is explored in a Josephson junction system driven by multiplicative and additive trichotomous noises in this paper. Under the adiabatic approximation, the analytical expression of average output current for the Josephson junction is obtained, which can be used to characterize stochastic resonance (SR). If only the additive trichotomous noise is considered, the large correlation time of additive noise can induce the suppression and the SR in the curve of average output current. When the effects of both multiplicative and additive trichotomous noises are considered, two pronounced peaks exist in the curves of average output current for large multiplicative noise amplitude and optimal additive noise intensity. That is, the stochastic multi-resonance phenomenon is observed in this system. Moreover, the curve of average output current appears a single peak as a function of multiplicative noise intensity, which disappears for the case of small fixed additive noise amplitude. Especially, the mean first-passage time (MFPT) as the function of additive trichotomous noise intensity displays a non-monotonic behavior with a maximum for the large multiplicative noise amplitude, which is called the phenomenon of the noise enhanced stability (NES).

Tempered Mittag-Leffler noise-induced resonant behaviors in the generalized Langevin system with random mass

In this study, we propose the fluctuating-mass generalized Langevin equation (GLE) with a tempered Mittag-Leffler (M-L) noise, and investigate the generalized stochastic resonance (GSR) phenomena in terms of output amplitude amplification. Based on numerical results, we study the dependence on various parameters systematically, and further discuss the interplay between memory exponent, memory time and tempering parameter, which diversifies the stochastic multi-resonance (SMR), including double-peak GSR, triple-peak GSR and quadruple-peak GSR. It is worth emphasizing that the latter two SMR phenomena have not been observed in the GLE with tempered fractional Gaussian noise. Moreover, as a generalization with tempered M-L noise, the conventional GLEs with M-L memory kernel, power-law memory kernel, or exponent-form memory kernel, can be effectively derived as the special cases of tempered M-L memory kernel. Thus, these results also provide more extensive support for manipulating the GSR behaviors through system parameter control in the potential applications.

Mittag-Leffler noise induced resonance behavior in a fractional generalized Langevin equation with random trichotomous inherent frequency

The resonance behavior in a generalized Langevin equation and fractional generalized Langevin equation with random trichotomous inherent frequency and a generalized Mittag-Leffler noise are extensively investigated. An expression for the noise spectral of the generalized Mittag-Leffler noise is studied. Using the Shapiro–Loginov formula and Laplace transformation technique, exact expressions for the spectral amplification of generalized Langevin equation and fractional generalized Langevin equation are obtained. The simulation results turn out to show that the spectral amplification is a non-monotonic function of the characteristics of noise parameters and system parameters. In particular, the influence of generalized Mittag-Leffler noise is able to induce the generalized stochastic resonance phenomenon. The influence of the driving frequency is able to induce bona fide stochastic resonance and stochastic multi-resonance phenomena. It is found that the resonance behavior of the fractional generalized Langevin equation has more material results than that of the (non-fractional) generalized Langevin equation.

Stochastic resonance in multi-stable coupled systems driven by two driving signals

The stochastic resonance (SR) in multi-stable coupled systems subjected to Gaussian white noises and two different driving signals is investigated in this paper. Using the adiabatic approximation and the perturbation method, the coupled systems with four-well potential are transformed into the master equations and the amplitude of the response is obtained. The signal-to-noise ratio (SNR) is calculated numerically to demonstrate the occurrence of SR. For the case of two driving signals with different amplitudes, the interwell resonance between two wells S1 and S3 emerges for strong coupling. The SR can appear in the subsystem with weaker signal amplitude or even without driving signal with the help of coupling. For the case of two driving signals with different frequencies, the effects of SR in two subsystems driven by high and low frequency signals are both weakened with an increase in coupling strength. The stochastic multi-resonance phenomenon is observed in the subsystem subjected to the low frequency signal. Moreover, an effective scheme for phase suppressing SR is proposed by using a relative phase between two driving signals.

Stochastic Multiresonance for a Fractional Linear Oscillator with Quadratic Trichotomous Noise**Supported by National Natural Science Foundation of China under Grant No. 61134002

The stochastic multiresonance behavior for a fractional linear oscillator with random system frequency is investigated. The fluctuation of the system frequency is a quadratic trichotomous noise, the memory kernel of the fractional oscillator is modeled as a Mittag–Leffler function. Based on linear system theory, applying Laplace transform and the definition of fractional derivative, the expression of the system output amplitude (SPA) is obtained. Stochastic multiresonance phenomenon is found on the curves of SPA versus the memory time and the memory exponent of the fractional oscillator, as well as versus the trichotomous noise amplitude. The SPA depends non-monotonically on the stationary probability of the trichotomous noise, on the viscous damping coefficient and system characteristic frequency of the oscillator, as well as on the driving frequency of external force.

Stochastic resonance in a delayed triple-well potential driven by correlated noises.

In this paper, we investigate stochastic resonance (SR) in a delayed triple-well potential subject to correlated noises and a harmonic signal. The stationary probability density, together with the response amplitude of the system, is obtained by using the small time delay approximation. It is found that the time delay, noise intensities, and the cross-correlation between noises can induce the occurrence of the transition. Moreover, the appropriate choice of noise intensities and time delay can improve the output of the system, enhance the SR effect, and lead to the phenomenon of noise enhanced stability. Especially, the stochastic multi-resonance phenomenon is observed when the multiplicative and additive noises are correlated. Finally, the theoretical results are well verified through numerical simulations.

STOCHASTIC MULTIRESONANCE INDUCED BY ADDITIVE AMPLITUDE MODULATION SIGNAL AND NOISE IN A GENE TRANSCRIPTIONAL REGULATORY MODEL

We investigate the stochastic resonance (SR) and stochastic multiresonance phenomena in a gene transcriptional regulatory system driven by additive amplitude modulation signal and cross-correlated noise. By using the general two-state approach, we obtained the analytic expression of signal-to-noise ratio (SNR) under the condition of adiabatic approximation. Our results show that the SR phenomenon can be observed and the peak of SR can be manipulated by the amplitude modulation deepness and the amplitude modulation frequency of the signal. More interestingly, stochastic multiresonance can be observed in the curve of SNR versus cross-correlation coefficient. Our results illustrate the potential to utilize the cross-correlation noise for controlling SNR under fixed noise intensity in the study of stochastic gene transcriptional regulatory process.

Damping Coefficient Induces Stochastic Multiresonance in Bistable System with Asymmetric Dichotomous Noise

Stochastic resonance (SR) and stochastic multiresonance (SMR) phenomena as a function of the underdamping and overdamping coefficients in bistable system with asymmetric dichotomous noise are investigated numerically. By the efficient numerical simulation of the asymmetric dichotomous noise and the fourth-order Runge-Kutta algorithm, we calculate the system responses, the averaged power spectrum, and the signal-noise-ratio (SNR) that can be a measure of the existence of SR and SMR phenomenon. And the effects of damping coefficients on the three characteristics are analyzed. Firstly, it is found that the periodic asymmetric distribution of the particle’s hopping between two potential wells in the system response is gradually weakened as underdamping coefficient is increased to overdamping coefficient. And it also displays the periodic asymmetric distribution under the circumstance of overdamping coefficient. Then the averaged power spectrum exhibits multiple sharp peaks, and the highest peak increases and decreases for underdamping coefficient which is added to overdamping coefficient. Finally, SNR versus the damping coefficient for the system parameters and the noise parameters are acquired and they show multiple peaks and valleys, which illustrates the obvious SMR phenomena in bistable system with asymmetric dichotomous noise.

Stochastic multi-resonance in an overdamped bistable system with two types of modulation signal

The stochastic resonance (SR) phenomenon in an overdamped bistable system with multiplicative and additive noise is investigated. The signal-to-noise ratio (SNR) is calculated when two types of modulation signal are added to the system. The effects of the intensities, the frequencies and relative phase shift of two types of modulation signal on the SNR are discussed, respectively. Research results show that: (i) the intensities of two types of modulation signal can enhance the maximum in the SNR as a function of the noise intensity, and the frequencies can restrain it; (ii) the additive modulation signal can enhance the maximum in the SNR as a function of the noise intensity in comparison with the multiplicative modulation signal; (iii) when both modulation frequencies are equal, the SNR as a function of the relative phase shift exhibits multiple maxima. The multiple maxima in the SNR identifies the characteristic of the stochastic multi-resonance phenomenon.