Stochastic resonance of a damped oscillator with frequency fluctuation driven by a periodic external force

<正>Considering a damped linear oscillator model subjected to a white noise with an inherent angular frequency and a periodic external driving force,we derive the analytic expression of the first moment of output response,and study the stochastic resonance phenomenon in a system.The results show that the output response of this system behaves as a simple harmonic vibration,of which the frequency is the same as the external driving frequency,and the variations of amplitude with the driving frequency and the inherent frequency present a bona fide stochastic resonance.     

Effect of Correlation of Two Dichotomous Noises on Stochastic Resonance

The effect of the correlation of two dichotomous noises on stochastic resonance is investigated for a linear stochastic system subject to a periodic oscillatory signal. It is found that, the correlation between the two dichotomous noises can not only affect the appearance of the stochastic resonance phenomenon, but also the distinctness of the stochastic resonance phenomenon. There is an optimal value of the correlation, at which the stochastic resonance phenomenon is most distinct. In addition, the correlation between the two dichotomous noises can also cause the movement of the peak of stochastic resonance. Finally, two stochastic resonances caused by two correlated multiplicative dichotomous noises can be found in this system.     

Resonance, Multi-resonance, and Reverse-resonance Induced by Multiplicative Dichotomous Noise

A constant-potential system driven by multiplicative dichotomous noise and subject to an input oscillatory signal is investigated. Two phenomena of stochastic resonance are observed. One is the response as a function of the noise＇s parameters; the other is that as a function of the input signal frequency. A phenomenon of multi-resonance （there are three or four peaks） is found for the response as a function of a parameter of the noise. A phenomenon of reverse-resonance is found, for which the response of the system to the signal can be weakened by the presence of the noise （there is an optimal minimum）. These results help in studies of the systems with multiplicative dichotomous noise, such as the semiconductor, the proteins motor, the chemical reaction, and so on.     

Entropic Stochastic Resonance Driven by Colored Noise

The phenomenon of entropic stochastic resonance （ESR） in a two-dimensional confined system driven by a transverse periodic force is investigated when the colored fluctuation is included in the system. Applying the method of unified colored noise approximation, the approximate Fokker-Planck equation can be derived in the absence of the periodic force. Through the escaping rate of the Brownian particle from one well to the other, the power spectral amplification can be obtained. It is found that increasing the values of the noise correlation time and the signal frequency can suppress the ESR of the system.     

Principal resonance response of a stochastic elastic impact oscillator under nonlinear delayed state feedback

In this paper, the principal resonance response of a stochastically driven elastic impact(EI) system with time-delayed cubic velocity feedback is investigated. Firstly, based on the method of multiple scales, the steady-state response and its dynamic stability are analyzed in deterministic and stochastic cases, respectively. It is shown that for the case of the multivalued response with the frequency island phenomenon, only the smallest amplitude of the steady-state response is stable under a certain time delay, which is different from the case of the traditional frequency response. Then, a design criterion is proposed to suppress the jump phenomenon, which is induced by the saddle-node bifurcation. The effects of the feedback parameters on the steady-state responses, as well as the size, shape, and location of stability regions are studied. Results show that the system responses and the stability boundaries are highly dependent on these parameters. Furthermore, with the purpose of suppressing the amplitude peak and governing the resonance stability, appropriate feedback gain and time delay are derived.     

Multiplicative Stochastic Resonance for a Linear System Driven by O-U Noise

In the paper, we study a linear system driven by O-U noise and give a method which is different from the one stated in Europhys. Lett. 40 （1997） 117. We find the same phenomenon of multiplicative stochastic resonance for the response of the system to the signal as the one found in Europhys. Left. 40 （1997） 117. The merit of our method is that it prevents the complex formulas when making sum from n = 0 to n →∞ as in Europhys. Lett. 40 （1997） 117, which leads to the approximate results of the figures.     

Control of stochastic resonance in bistable system by using periodic signal

<正>According to the characteristic structure of double wells in bistable systems,this paper analyses stochastic fluctuations in the single potential well and probability transitions between the two potential wells and proposes a method of controlling stochastic resonance by using a periodic signal.Results of theoretical analysis and numerical simulation show that the phenomenon of stochastic resonance happens when the time scales of the periodic signal and the noise-induced probability transitions between the two potential wells achieve stochastic synchronization.By adding a bistable system with a controllable periodic signal,fluctuations in the single potential well can be effectively controlled,thus affecting the probability transitions between the two potential wells.In this way,an effective control can be achieved which allows one to either enhance or realize stochastic resonance.     

Stochastic resonance and nonequilibrium dynamic phase transition of Ising spin system driven by a joint external field

The dynamic response and stochastic resonance of a kinetic Ising spin system （ISS） subject to the joint action of an external field of weak sinusoidal modulation and stochastic white-nolse are studied by solving the mean-field equation of motion based on Glauber dynamics. The periodically driven stochastic ISS shows that the characteristic stochastic resonance as well as nonequilibrium dynamic phase transition （NDPT） occurs when the frequency ω and amplitude h0 of driving field, the temperature t of the system and noise intensity D are all specifically in accordance with each other in quantity. There exist in the system two typical dynamic phases, referred to as dynamic disordered paramagnetic and ordered ferromagnetic phases respectively, corresponding to a zero- and a unit-dynamic order parameter. The NDPT boundary surface of the system which separates the dynamic paramagnetic phase from the dynamic ferromagnetic phase in the 3D parameter space of ho-t-D is also investigated. An interesting dynamical ferromagnetic phase with an intermediate order parameter of 0.66 is revealed for the first time in the ISS subject to the perturbation of a joint determinant and stochastic field. The intermediate order dynamical ferromagnetic phase is dynamically metastable in nature and owns a peculiar characteristic in its stability as well as the response to external driving field as compared with a fully order dynamic ferromagnetic phase.     

Stochastic resonance in an over-damped linear oscillator

For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function,we study the stochastic resonance(SR) in this paper. Using the Shapiro–Loginov formula, we acquire the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, we obtain the analytical expression of the output signal-to-noise ratio(SNR). Meanwhile, we discuss the evolutions of the SNR with the signal frequency, noise intensity, correlation rate of noise, time period, and modulation frequency. We find a new bona fide SR. The evolution of the SNR with the signal frequency presents periodic oscillation, which is not observed in a conventional linear system. We obtain the conventional SR of the SNR with the noise intensity and the correlation rate of noise. We also obtain the SR in a wide sense, in which the evolution of the SNR with time period modulation frequency presents periodic oscillation. We find that the time-periodic modulation of the cross-correlation intensity between noises diversifies the stochastic resonance phenomena and makes this system possess richer dynamic behaviors.