双稳系统的频率耦合与随机共振机理

分析了处于双势阱中的粒子在单一频率信号和双频信号作用下的运动形式,给出在双频信号作用下双稳系统的响应幅值与激励幅值的近似解析关系,揭示了非线性系统所特有的不同频率之间的频率耦合现象和激励输入的频率能量向另一频率转移的渗透现象.从动力学机理和频谱分布的角度进行分析,深化了对双稳系统随机共振机理的认识.数值仿真结果证明了理论分析的有效性.     

双稳随机共振参数特性的研究

以双稳系统为研究对象，探讨了影响和产生双稳随机共振的参数选择特性.双稳系统参数和二次采样频率参数有着内在的物理联系，它们的改变都会引起势垒、势阱间距和粒子跃迁速率的改变，并使噪声能量相对重新分配，进而影响随机共振效果.根据随机共振的参数选择规律，可通过适当的参数选择来得到最佳的随机共振状态，为后续数据处理奠定基础.     

三态噪声激励下分数阶耦合系统的随机共振现象

为了刻画在黏弹性介质中具有质量涨落的耦合粒子的运动行为,本文提出了相应模型,即三态噪声激励下的分数阶耦合系统.利用Shapiro-Loginov公式和Laplace变换,发现了粒子间的统计同步性,并得到了系统输出幅值增益的解析表达.在此基础上,针对模型涉及的关键要素,即耦合系统、分数阶系统和三态噪声,着重分析了耦合系数、系统阶数和噪声稳态转移概率对系统输出幅值增益的广义随机共振现象的影响,并给出了合理解释.具体地说,1)随着耦合系数的增大,共振现象将先增强后减弱,直至收敛.该现象表明适当的耦合作用能够促进系统共振现象的产生,体现了研究耦合系统的重要性.2)随着系统阶数的增大,共振现象将逐渐减弱.当系统阶数取值为1,即系统退化为整数阶系统时,其输出幅值增益的峰值最小,该现象说明分数阶系统能比传统整数阶系统得到更大的输出幅值增益.3)噪声稳态转移概率对系统输出幅值增益的影响会随着与之相关的其他参数的变化而变化.在一定参数条件下,三态噪声不仅能够使系统输出幅值获得比双态噪声激励时更大的增益,还能改变系统的共振类型.最后,通过数值仿真验证了上述结果的正确性.     

双稳系统随机共振的反馈控制

将双稳系统的输出反馈到输入端再作用于系统,提出了采用反馈来控制随机共振的方法.以典型双稳系统为对象,并以信噪比和功率谱放大率作为度量随机共振效应的可观察变量,分别研究了采用线性或非线性反馈函数所产生的随机共振现象.理论分析和数值仿真结果表明随机共振是可控制的.该方法特别适用于系统参数固定或难以改变的系统. 关键词： 双稳系统 随机共振 反馈控制 共振效应     

双稳系统随机共振的能量输入机理

从布朗粒子运动所遵循的Langevin方程出发,分析了周期性外力提供给布朗粒子的瞬时功率和平均功率．揭示了双稳系统随机共振的能量输入机理．理论分析与数值仿真结果表明,布朗粒子吸收的瞬时功率随时间作周期性变化,其变化的频率是周期性外力的2倍,而其幅值和均值的大小都受控于噪声强度．改变布朗粒子所处热环境的参数,能有效地控制周期性外力的能量输入形式．     

耦合双稳系统的随机共振控制

两个双稳系统经非线性耦合而成为多稳态系统,该耦合系统与单一双稳系统相比具有较高的理论研究和实际应用价值.解析地分析了耦合系统在含噪弱周期信号作用下的响应特性,给出了耦合系数和双稳系统参数对随机共振的影响,表明耦合系统的随机共振是在带状的双势阱作用下产生的,还构建了反馈耦合控制原理框图.这为在双稳类系统中人为地产生随机共振或使共振效应更加强烈即随机共振的控制及其应用提供了可靠的理论依据.数值仿真结果与理论分析完全符合. 关键词： 耦合双稳系统 随机共振 控制     

力与耦合系统的交互作用和随机能量共振

外界对系统作功的过程就是系统状态发生变化的过程.根据Langevin方程的随机动力学特性,采用微观动力学和宏观热力学方法,建立了基于单一随机轨线的耦合双稳系统的热力学关系.通过力与耦合系统的功交互作用定量地刻画了能量的传递和转换关系,揭示了耦合系统中存在着的随机能量共振现象.从作功与能量的关系进行分析,进一步揭示了随机共振产生的物理本质. 关键词： 耦合双稳系统 随机热力学 随机能量共振 功     

双稳系统演化的时间尺度与随机共振的加强

噪声作用下的双稳系统存在着单一势阱内的随机波动和两势阱之间的概率跃迁,这两种不同层级的运动具有不同的时间尺度,且低层级的势阱内的波动影响着高层级的势阱间的跃迁．当外作用周期信号的时间尺度与噪声诱导的势阱间概率跃迁达到随机同步时,则能产生随机共振;给系统再加第二驱动周期信号,使其时间尺度与低层级的势阱内的波动相匹配,则存在着频率吸收现象,并能增强双稳系统的随机共振效应． 关键词： 随机共振 双稳系统 层级 时间尺度     

随机共振的模拟实验

用模拟电路的方法对随机共振现象进行多方面的实验研究,讨论随机共振机制,测量输出信噪比(SNR),由于在随机共振过程中部分噪声能量可转变为信号能量,利用这个机制可能在强噪声对信号的抑制下取出信号。 关键词：     

双稳系统的随机能量共振和作功效率

分析了处于双稳系统中的布朗粒子与外界的周期性外力和热随机力的功、热交互作用,建立了基于Langevin方程的随机能量平衡方程.围绕着受周期力、随机力和阻尼力共同作用的Langevin方程,采用动力学和非平衡热力学相结合的方法,从以"力"为立足点转到以"能量"为研究核心,深入分析了布朗粒子沿单一轨线运动时系统与环境之间的能量交换和作功效率,揭示了双稳系统的随机能量共振现象. 关键词： 双稳系统 随机能量共振 作功效率     

Frequency-Dependent Stochastic Resonance in Globally Coupled Systems

A model of globally coupled bistable systems consisting of two kinds of sites, subject to a periodic driving and spatially uncorrelated stochastic force, is investigated. In the large system size limit, the problem of large number of coupled Langevin equations can be reduced to a simple problem of two coupled ordinary differential equations. Considering the finite size effect, we can derive two coupled Langevin equations. All the above three kinds of equations are numerically computed and compared with each other. Fkequency-dependent stochastic resonance is found, and the reduced equations can represent the high-dimensional system when the system size is large.     

Stochastic Resonance in a Bistable System Subject to Non-Gaussian and Gaussian Noises

In this paper, we consider the phenomenon of stochastic resonance （SR） in a quartic bistable system under the simultaneous action of a multiplicative non-Gaussian and an additive Gaussian noises and a weak periodic signal. The expression of the signal-to-noise ratio R is derived by applying the two-state theory in adiabatic limit. We discuss the effects of the parameter q indicating the departure of the non-Gaussian noise from the Gaussian noise, the correlation time r of the non-Gaussian noise, and coupling intensity A between two noise terms on the stochastic resonance. It is found that the signM-to-noise ratio of the system, as a function of the additive noise intensity, undergoes the transition from having one peak to having two peaks, and then to having one peak again when the parameter q or the noise correlation time τ is increased. The parameter q and τ play opposite roles in the SR of the system.     

Stochastic Resonance in a Bistable System Subject to Dichotomous Noise

The stochastic resonance phenomenon in a bistable system subject to Markov dichotomous noise （DN） is investigated. Based on the adiabatic elimination and the two-state theories, the explicit expressions for the signal-tonoise ratio （SNR） and the spectral power amplification （SPA） have been obtained. It is shown that two peaks can occur on the curve of SNR versus the intensity of the DN. Moreover, the SNR is a non-monotonic function of the correlation time of the DN. The SPA varies non-monotonously with the strength of the DN. The dependence of the SNR on the frequency and the amplitude of the external periodic signal are discussed. The effect of the external frequency and the correlation time of the DN on the SPA are analyzed.     

Stochastic Resonance in a Bistable System Subject to Dichotomous Noise

The stochastic resonance phenomenon in a bistable system subject to Markov dichotomous noise (DN) is investigated. Based on the adiabatic elimination and the two-state theories, the explicit expressions for the signal-to-noise ratio (SNR) and the spectral power amplification (SPA) have been obtained. It is shown that two peaks can occur on the curve of SNR versus the intensity of the DN. Moreover, the SNR is a non-monotonic function of the correlation time of the DN. The SPA varies non-monotonously with the strength of the DN. The dependence of the SNR on the frequency and the amplitude of the external periodic signal are discussed. The effect of the external frequency and the correlation time of the DN on the SPA are analyzed.     

Stochastic Resonance in a Bistable System with Time-Delayed Feedback Loops

The phenomenon of stochastic resonance of a bistable system subjected to linear time-delayed feedback loops driven by multiplieative Gaussian coloured noise and additive Gaussian white noise is investigated. Firstly, the analytic expression of the quasi-steady distribution function Ps （x, t） is derived by applying the unified coloured noise approximation and the Novikov Theorem; Secondly, the expression of the signal-to-noise ratio （SNR） is obtained in the adiabatic limit to quantify the stochastic resonance. Finally, tile effects of the linear coefficient a, the nonlinear coefficient b, the linear time-delayed feedback coefficient c and the delay time r on Ps（x,t） and SNR^± are discussed. It is found that the effects of the linear coefficient and the nonlinear coefficient, the positive linear time-delayed feedback coefficient and the negative linear time-delayed feedback coefficient, the positive delayed time and the negative delayed time on Ps（x,t） and SNR^± are different, respectively. This discussion would be helpful to the study of the system reliability and controlling stochastic resonance.     

New Characterization of Stochastic Resonance in Bistable Square Potential Well

The features of first passage time density function is analysed theoretically in a symmetric double square well system modulated periodically with a signal of arbitrary amplitude and frequency. Resonance is demonstrated as a maximum synchronization between periodic signal and noise. Resonance is characterized as a linear relation between noise strength at resonance and frequency. This characterization is shown to hold good for amplitude lesser or greater than the depth of the unmodulated potential well. The mean first passage time of the process at resonance is also shown to decrease linearly with the strength of the noise for high amplitude of the signal while it increases linearly with inverse of the noise strength for low amplitude.     

Stochastic Resonance of a Periodically Driven Bistable System with Two Different Kinds of Time Delays

In this paper, we study the phenomenon of stochastic resonance （SR） in a periodically driven bistable system with correlations between multiplicative and additive white noise terms when there, are two different kinds of time delays existed in the deterministic and fluctuating forces, respectively. Using the small time delay approximation and the theory of signal-to-noise ratio （SNR） in the adiabatic limit, the expression of SNR is obtained. The effects of the delay time T in the deterministic force, and the delay time 8 in the fluctuating force on SNR are discussed. Based on the numerical computation, it is found that： （i） There appears a reentrant transition between one peak and two peaks and then to one peak again in the curve of SNR when the value of the time delay θ is increased. （ii） SR can be realized by tuning the time delay T or 8 with fixed noise, i.e., delay-induced stochastic resonance （DSR） exists.     

Stochastic Resonance of a Periodically Driven Bistable System with Two Different Kinds of Time Delays

In this paper, we study the phenomenon of stochastic resonance (SR) in a periodically driven bistable system with correlations between multiplicative and additive white noise terms when there are two different kinds of time delays existed in the deterministic and fluctuating forces, respectively. Using the small time delay approximation and the theory of signal-to-noise ratio (SNR) in the adiabatic limit, the expression of SNR is obtained. The effects ofthe delay time τ in the deterministic force, and the delay time θ in the fluctuating force on SNR are discussed. Based on the numerical computation, it is found that: (i) There appears a reentrant transition between one peak and two peaks and then to one peak again in the curve of SNR when the value of the time delay θ is increased. (ii) SR can be realized by tuning thetime delay τ or θ with fixed noise, i.e., delay-inducedstochastic resonance (DSR) exists.     

Array-enhanced logical stochastic resonance subject to colored noise

This paper proposes an approach that uses a parallel array to improve the reliability and robustness of logical stochastic resonance subject to colored noise. The experimental results demonstrate that (i) the increase of array size can extend the optimal range of noise intensity and increase the maximum probability of obtaining correct logic operation. (ii) The optimal range of noise correlation time is broadened with the increase of array size. (iii) The main difference between logical stochastic resonance subject to white noise and colored noise is that the increase of noise correlation time broadens the optimal range of noise intensity when the stochastic noise is colored noise. At the same time, the maximum probability of obtaining correct logic operation is close to 1. Therefore, reliable and robust logic gate can be realized under a certain array size.     

Appearance of Stochastic Resonance in Protein Motor System

A protein motor system driven by sine electric field is investigated. The signal-to-noise ratio （SNR） is derived in the adiabatic limit. The phenomenon of stochastic resonance is found for this protein motor system.