关联噪声驱动的非对称双稳系统的随机共振

运用统一色噪声近似理论和两态模型理论,研究了周期矩形信号和关联的乘性色噪声和加性白噪声驱动的非对称双稳系统的随机共振现象,得到了适合信号任意幅值的信噪比表达式.信噪比是乘性噪声强度、加性噪声强度、乘性噪声自关联时间、噪声耦合强度的非单调函数,所以该双稳系统中出现了随机共振.同时,调节加性噪声强度比调节乘性噪声强度更容易产生随机共振.势阱静态非对称性和噪声之间的耦合强度对信噪比的影响是不同的. 关键词： 非对称双稳系统 随机共振 信噪比 周期矩形信号     

Arrays of noisy bistable elements with nearest neighbor coupling: equilibrium and stochastic resonance

This work deals with finite arrays of bistable systems with nearest neighbor coupling. We focus on the statistical equilibrium of a collective variable, as well as its response to a weak time periodic perturbation. By means of numerical simulations we demonstrate the sharp contrast between the system behaviors depending on whether the coupling parameter is positive or negative. The stochastic resonance phenomenon is analyzed in terms of the power spectral amplification and the signal-to-noise ratio of the collective variable. Even though those quantifiers show the typical non-monotonic dependence on the noise strength, they lack, for negative coupling, the large enhancement which has been previously observed for arrays with positive coupling.     

Stochastic resonance in a bistable system with coloured correlation between additive and multiplicative noise

The phenomenon of stochastic resonance (SR) in a bistable nonlinear system with coupling between additive and multiplicative noises is investigated when the correlation between two noise terms is coloured. It is found that the signal-to-noise ratio (SNR) of the system is affected not only by the coupling strength λ between two noise terms, but also by the noise correlation time τ. The SNR is changed from a single peak, to two peaks with a dip, and then to a monotonically decreasing function with noise strength. The dependence of the SR on the initial conditions is entirely caused by the coupling strength λ between two noise terms.     

周期混合信号和噪声联合激励下的非对称双稳系统的随机共振

研究了周期混合信号和关联的乘性和加性噪声联合激励下的非对称双稳系统的随机共振现象.运用两态理论,给出了基频和高阶谐频信噪比的理论结果.发现对于基频和高阶谐频情形下均出现随机共振，并且高阶谐频存在抑制现象.同时研究了非对称系数和噪声强度以及噪声之间关联强度对信噪比的影响.     

由加性和乘性噪声驱动的非对称双稳系统的随机共振

根据信噪比理论，研究了由乘性和加性白噪声以及周期矩形信号共同作用的非对称双稳系统的随机共振。推导出了信噪比的解析表达式，并且该表达式适用于任意的信号振幅。数值分析表明乘性噪声强度D和加性噪声强度α对信噪比的影响是不同的：对应于任意的一个非对称系数r的值，SNR-α 曲线比SNR-D曲线更容易出现随机共振。即当系统的双阱不是很不对称的时候，改变加性噪声比改变乘性噪声更容易产生随机共振。此外，势井的非对称性能够减小信噪比。     

Long-Time Dynamic Response and Stochastic Resonance of Subdiffusive Overdamped Bistable Fractional Fokker--Planck Systems

To explore the influence of anomalous diffusion on stochastic resonance （SR） more deeply and effectively, the method of moments is extended to subdiffusive overdamped bistable fractional Fokker-Planck systems for calculating the long-time linear dynamic response. It is found that the method of moments attains high accuracy with the truncation order N = 10, and in normal diffusion such obtained spectral amplification factor （SAF） of the first-order harmonic is also confirmed by stochastic simulation. Observing the SAF of the odd-order harmonics we find some interesting results, i.e. for smaller driving frequency the decrease of subdiffusion exponent inhibits the stochastic resonance （S.R）, while for larger driving frequency＂ the decrease of subdiffusion exponent enhances the second SR peak, but the first one vanishes and a double SR is induced in the third-order harmonic at the same time. These observations suggest that the anomalous diffusion has important influence on the bistable dynamics.     

Stochastic resonance in multi-scale bistable array

This Letter explores a new mechanism of stochastic resonance (SR) that is induced by the multi-scale noise decomposed from the input signal, which is promising in signal detection and processing under heavy background noise. The input signal is firstly decomposed to multi-scale signals by orthogonal wavelet transform. Then, the approximate signal, which contains the driving signal, is processed by an uncoupled parallel bistable array with the detailed signal of each scale as the internal noise. At last, a SR mechanism combining the effects of colored noise and array SR is proposed. The simulation results show that a high quality output signal can be obtained by the new mechanism. The proposed model is more adaptive to input signal with high noise intensity than single bistable SR system, which can be seen from the signal-to-noise ratio curves and average noise intensity curves.     

Influence of Delayed-Time and Colored-Noise in a Bistable System Subject to Asymmetric Dichotomous Noise and Colored Noise

The influence of delayed-time and colored-noise in a bistable system subject to asymmetric dichotomous noise and colored noise is studied. Applying small delay-time approximation, under the adiabatic limit condition, the expression of the signal-to-noise ratio (SNR) of the system is obtained. It is found that, the SNR varies non-monotonously with the delayed-time and the correlation of the colored noise. Moreover, the SNR exhibits SR behavior when it is plotted as a function of the intensity and asymmetry of the dichotomous noise, and as a function of the strength of the colored noise.     

Dynamical complexity and stochastic resonance in an asymmetry bistable system with time delay

The dynamical complexity and stochastic resonance (SR) of a time-delayed asymmetric bistable system are studied. Firstly, The effective potential function and steady-state probability density function are deduced based on Born-Oppenheimer approximation theory, and we find that the asymmetric item and time-delayed feedback item can both affect the curve of these two functions, especially the asymmetric item can induce phase displacement. Secondly, the mean first-passage time (MFPT) which plays an important role in research on particles escape rate is derived and we obtain an approximate asymmetric item r which can maintain a steady MFPT. Finally, the influences of different parameters on SR are researched by signal-to-noise ratio (SNR). The analytic expression of SNR is derived and three dimensional graphs and contour maps of SNR with different parameters are obtained. The results indicate that time delay τ and time delay strength e can enhance the SNR and the asymmetric item r has a non-monotone effect on SNR. Notably, adjusting time delay strength e is more sensitive than that of the time delay τ in controlling SR.     

Circuit QED and sudden phase switching in a superconducting qubit array

Superconducting qubits connected in an array can form quantum many-body systems such as the quantum Ising model. By coupling the qubits to a superconducting resonator, the combined system forms a circuit QED system. Here, we study the nonlinear behavior in the many-body state of the qubit array using a semiclassical approach. We show that sudden switchings as well as a bistable regime between the ferromagnetic phase and the paramagnetic phase can be observed in the qubit array. A superconducting circuit to implement this system is presented with realistic parameters.     

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.     

Stochastic resonance in an asymmetric bistable system driven by coloured correlated multiplicative and additive noise

This paper investigates the stochastic resonance （SR） phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured. The approximate expression of signal-to-noise ratio has been obtained by applying the two-state theory and SR exhibits in the bistable system. Moreover, the potential asymmetry r and cross-correlation strength λ can weaken the SR phenomenon, while the cross-correlation time r can strengthen the SR phenomenon.     

Stochastic resonance in an asymmetric bistable system with coloured noises and periodic rectangular signal

In this paper, we consider the phenomenon of stochastic resonance (SR) in an asymmetric bistable system with coloured noises and periodic rectangular signal. Expression of the signal-to-noise ratio (SNR) has been obtained under the adiabatic limit. We investigate the effect of any system parameter (such as p, q, r, τ₁, τ₂) on the SNR. The plot of SNR-τ₁ shows SR for some values of the additive noise self-correlation time τ₂, but not for the whole range of τ₂. The system bias r suppresses the SNR. When the intensity of additive noise q is increased, the SR phenomenon disappears in the plot of SNR-p, but the plot of SNR-q presents SR for almost all values of the multiplicative noise intensity p.     

光学双稳系统中的随机共振

运用绝热近似理论，研究了由加性噪声和乘性噪声及周期信号驱动的光学双稳系统的随机共振现象. 发现该模型中输出信噪比R～随着加性噪声强度D_a的变化曲线中会出现随机共振现象，而信噪比R～随着乘性噪声强度D_m的变化曲线是单调减小的，信噪比曲线中没有出现随机共振现象. 因此，加性噪声和乘性噪声对输出信噪比的影响是不同的. 关键词： 随机共振 信噪比 乘性噪声 加性噪声     

Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal

Stochastic resonance(SR) is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory(LRT), the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density(PSD) and signal-to-noise ratio(SNR) are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.     

Stochastic resonance in bistable confining potentials

We study the effects of the confining conditions on the occurrence of stochastic resonance (SR) in continuous bistable systems. We model such systems by means of double-well potentials that diverge like |x|^q for |x|↦∞. For super-harmonic (hard) potentials with q > 2 the SR peak sharpens with increasing q, whereas for sub-harmonic (soft) potentials, q < 2, it gets suppressed.     

System size stochastic resonance in driven finite arrays of coupled bistable elements

The global response to weak time periodic forces of an array of noisy, coupled nonlinear systems might show a nonmonotonic dependence on the number of units in the array. This effect has been termed system size stochastic resonance by other authors. In this paper, we focus on a collective variable of a finite array of one-dimensional globally coupled bistable elements. We analyze the possible nonmonotonic dependence on the system size of its power spectral amplification and its signal-to-noise ratio.     

Stochastic resonance in time-delayed bistable systems driven by weak periodic signal

We study theoretically a bistable system with time-delayed feedback driven by a weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can change the shapes of the potential wells. In the adiabatic approximation, the signal-to-noise ratio (SNR) of the system with a weak periodic force is obtained. The time-delayed feedback modulates the magnitude of SNR by changing the shape of the potential and the effective strength of the signal. The maximum of SNR decreases with increasing the feedback intensity ?. When ? is negative (or positive), the time delay can suppress (or promote) the stochastic resonance phenomenon.