Effect of inertia mass on the stochastic resonance driven by a multiplicative dichotomous noise

A stochastic system driven by dichotomous noise and periodic signal is investigated in the under-damped case.The exact expressions of output signal amplitude and signal-to-noise ratio(SNR) of the system are derived.Numerical results indicate that the inertial mass greatly affects the output signal amplitude and the SNR.Regardless of whether the noise is symmetric or asymmetric,the inertial mass can influence the phenomenon of stochastic resonance(SR) of the system,leading to two types of resonance phenomenon:one is coherence-resonance-like of the SNR with inertial mass,the other is the SR of the SNR with noise intensity.     

Parameter-induced stochastic resonance in an over-damped linear system

Stochastic resonance (SR) in an over-damped linear system subjected to an excitation of bias signal modulated noise with multiplicative and additive noises is investigated. We obtain the exact expressions of the first two moments and the signal-to-noise ratio (SNR) of the output by using linear-response theory. The SNR depends non-monotonically on the intensity and the correlation time of multiplicative noise, the correlation time of additive noise, the intensity of the cross noise between multiplicative and additive noise, as well as the external field frequency. The conventional SR, the SR in a broad sense and the bona fide SR are found in the system. The influences of the asymmetries of multiplicative and additive noise, the correlation rate of the cross noise, the intensity of additive noise, the amplitude of signal and the bias on the SNR are analyzed. Moreover, we pointed out that SR can be realized by tuning the system parameter with fixed noise, i.e., parameter-induced stochastic resonance (PSR) exists.     

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。     

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     

Effects of combined harmonic and random excitations on a Brusselator model

We discuss the constructive role of combined harmonic and random excitation on stochastic resonance (SR) in a Brusselator model. We first numerically investigate SR determined by the Signal-to-Noise Ratio (SNR) in this model. Effects of different parameters on SR are described in detail. Our simulation results show that the intensity of the Gaussian colored noise and the amplitude of the periodic force can enhance SR. Moreover, an analytical framework is presented for the SNR of the Brusselator model, leading to a theoretical expression of SNR. We observe a good agreement between the theoretical and numerical results, and the effectiveness of the proposed theoretical method is verified. This theoretical analysis provides a global view on how the dynamics of a periodically forced system with noise changes in the vicinity of a Hopf bifurcation.     

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     

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.     

三稳系统的动态响应及随机共振

以平衡点参数p, q构造出一类对称三稳势函数, 进而提出微弱信号和噪声共同驱动的三稳系统模型. 深入研究并总结参数p, q对势垒高度ΔU₁, ΔU₂及两势垒高度差的影响. 从定常输入的角度提出了系统稳态解曲线的概念, 并进一步研究低频谐波信号输入时系统的输出动态响应. 引入噪声, 三稳系统在合适的参数条件下实现随机共振, 从稳态解曲线的角度分析了噪声诱导的三稳系统随机共振机理. 最后研究了阻尼比k和平衡点参数p, q对系统随机共振的影响.     

Effects of time delay on stochastic resonance of a periodically driven linear system with multiplicative and periodically modulated additive white noises

Stochastic resonance (SR) of a periodically driven time-delayed linear system with multiplicative white noise and periodically modulated additive white noise is investigated. In the condition of small delay time, an approximate analytical expression of output signal-to-noise ratio (SNR) is obtained. The analytical results indicate that (1) there exists a resonance peak in the curve for SNR versus time delay; (2) the time delay will suspend the SR dramatically for SNR versus other parameters of the system, such as noise intensity, correlation intensity, and signal frequency, once a certain value is reached, the SR phenomenon disappears.     

Stochastic Resonance in Linear Region of a Single-Mode Laser： Effects of Amplitude Modulation of Signal

A single-mode laser noise model driven by quadratic colored pump noise and amplitude modulation signal is proposed. The real and imaginary parts of the pump noise are assumed to be cross-correlation. The effect of cross-correlation of noise and amplitude modulation of signal on laser statistical properties is studied by using the linearized approximation. The analytic expression of signal-to-noise ratio (SNR) is calculated. It is found that the phenomena of stochastic resonance (SR) respectively exist in the curves of the SNR versus the noise cross-correlation coefficient λ and the SNR versus the pump parameter a, as well as the SNR versus the signal frequency ω in our model. It is shown that there are three different typies of SR in the model: the conventional form of SR, the SR in the broad sense, and the bona fide SR.     

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.     

Research on detection method of multi-frequency weak signal based on stochastic resonance and chaos characteristics of Duffing system

Weak signal detection has been widely used in many fields such as military and national economy. Aiming at the problem that the traditional stochastic resonance (SR) method can’t obtain the signal amplitude when detecting weak signals, the frequency and amplitude of the weak signal are obtained by combining the SR and chaos characteristics of the two-dimensional Duffing system. Firstly, the effects of two-dimensional Duffing system parameters a, b, k, noise intensity D on the Kramers rate and signal-to-noise ratio (SNR) are analyzed under the Gaussian white noise environment. The results show that the damping ratio K can hinder the SR effect of the system to some extent. Secondly, to solve the misjudgment of the state method of the weak signal amplitude in the detection, the Lyapunov exponent is used to assure the threshold's range, and the threshold of the chaotic critical state is found. Finally, the paper gives the processes of frequency and amplitude detection of multiple high-frequency signals, which realizes the effective detection of the frequency and amplitude of multiple high-frequency signals in a Gaussian white noise environment, and successfully applies the method to the accurate detection of boundary voltage amplitude in electrical impedance tomography.     

Stochastic resonance of bias signal-modulated noise in a single-mode laser＊

Stochastic resonance (SR) for bias signal modulation is studied in a single-mode laser system. By investigating a gain-noise model driven by correlated pump noise and quantum noise, we find that, whether the correlation coefficient between both the noises is positive or negative, SR always appears in the dependence of signal-to-noise ratio (SNR) upon the noise correlation time and the frequency of the modulation signal. However, only when the correlation coefficient between both noises is negative can SR occur in the dependence of SNR upon the quantum noise intensity and pump noise intensity, while when the correlation coefficient between both noises is positive, it shows monotonically.     

具有非线性阻尼涨落的线性谐振子的随机共振

较之于线性噪声, 非线性噪声更广泛地存在于实际系统中, 但其研究远不能满足实际情况的需要. 针对作为非线性阻尼涨落噪声基本构成成分的二次阻尼涨落噪声, 本文考虑了周期信号与之共同作用下的线性谐振子, 关注这类具有基本意义的阻尼涨落噪声的非线性对系统共振行为的影响. 利用Shapiro-Loginov公式和Laplace变换推导了系统稳态响应振幅的解析表达式, 并分析了稳态响应振幅的共振行为, 且以数值仿真验证了理论分析的有效性. 研究发现: 系统稳态响应振幅关于非线性阻尼涨落噪声系数具有非单调依赖关系, 特别是非线性阻尼涨落噪声比线性阻尼涨落噪声更有助于增强系统对外部周期信号的响应程度; 而且, 非线性阻尼涨落噪声比线性阻尼涨落噪声使得稳态响应振幅关于噪声强度具有更为丰富的共振行为; 同时, 二次阻尼涨落噪声使得稳态响应振幅关于系统频率出现真正的共振现象; 而在这些现象和性质中, 非线性噪声项的非线性性质对共振行为起着关键的作用. 显然, 以二次阻尼涨落作为基本形式引入的非线性阻尼涨落噪声, 可以有助于提高微弱周期信号检测的灵敏度和实现对周期信号的频率估计.     

偏置信号调制下色关联噪声驱动的线性系统的随机共振

研究了偏置信号调制下关联分段噪声驱动的过阻尼线性系统的随机共振现象，推导出了一阶矩、二阶矩和信噪比的解析表达式. 通过对信噪比曲线的分析，发现该系统中存在三种不同形式的随机共振：传统的随机共振、真正的随机共振和广义的随机共振. 此外，数值结果还表明，加性噪声能够减弱输出的信噪比，而噪声之间的互相关强度能够使输出的信噪比增强. 关键词： 随机共振 信噪比 偏置信号调制的噪声 分段噪声     

具有周期信号调制噪声的线性模型的随机共振

研究了具有周期信号调制噪声的过阻尼线性系统的随机共振现象.当采用非对称的分段噪声 时，可以得到系统响应的一、二阶矩和信噪比的精确表达式.通过对信噪比的分析, 发现了 “真实的"随机共振和传统的随机共振现象，讨论了乘性噪声的非对称性、自相关时间和噪 声之间的相关强度对信噪比的影响. 关键词： 随机共振 信噪比 周期信号调制噪声 线性模型     

Detection of multi-frequency weak signals with adaptive stochastic resonance system

Aiming at the poor detection rate of multi-frequency weak signals under a strong background of noise, a novel method based on adaptive stochastic resonance (SR) theory is proposed in this paper. The optimal parameters can be obtained automatically via measurement by establishing an adaptive SR system model and using the reverse location method. After passing through the adaptive SR system, the spectrum values of all eight signals greatly improve, the largest spectrum value gain increases from 12.41 to 2033 when the frequency is 0.01?Hz, which is an improvement of a factor of 162.8, and the signal-to-noise ratio (SNR) gain of the whole system is 10.3134?dB. Under the condition of different input noise intensities and signal amplitudes, the mean SNR of the system increases from –13.1136 to –2.7614?dB, which is a 78.9% increase, and the largest SNR gain is 13.4702?dB when the noise intensity D?=?1.2 and signal amplitude A?=?0.11. Compared to the single optimal spectrum value, when defining multiple optimum spectrum values as the SNR criterion, the detection sensitivity is less than 0.35 when the input noise intensity is between 0.5 and 2.5, and the sensitivity value is 6.29 times higher when D?=?2.5. The system successfully realizes the adaptive detection of twelve weak signals, and the SNR gain is 7.9743?dB, which improves the channel capacity of signal detection. The experimental results demonstrate the high efficiency and strong applicability of the system, improving the signal processing efficiency and speed of signal transmission.     

一阶线性系统的调参随机共振研究

分析了一阶线性系统在正弦和白噪声信号作用下的输出功率谱和信噪比.研究表明,加性噪声作用下的线性系统不存在传统意义上的随机共振,但却存在输出信噪比随系统参数非单调变化的调参广义随机共振现象.针对任意频率信号,分析了不同采样频率下的调参共振谱特性,得出适当增大采样频率有利于特征信号识别的结论.     

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.