双稳态系统中随机共振和相干共振的相关性

研究了加性噪声和乘性噪声共同驱动的双稳态系统中的随机共振和相干共振现象. 针对加性噪声和乘性噪声之间不存在关联性和存在关联性两种情形, 引入一种适当的能同时表征随机共振和相干共振的指标, 应用一阶欧拉方法, 通过数值模拟对系统的随机共振和相干共振现象进行研究. 结果表明在弱噪声驱动下, 随着加性噪声强度的增加, 当系统出现相干共振时, 如果给系统外加一个弱周期驱动力, 几乎在同一时刻, 系统也出现了随机共振现象; 但随着乘性噪声强度的增加, 仅当加性噪声和乘性噪声之间相关时, 此结论成立. 并且系统参数对相干共振和随机共振的影响是一致的. 关键词： 双稳态系统 随机共振 相干共振     

α稳定噪声环境下过阻尼系统中的参数诱导随机共振现象

本文采用随机模拟方法, 研究了过阻尼振子系统在α稳定噪声环境下的参数诱导随机共振现象. 结果表明, 在α噪声环境下, 调节系统参数能够诱导随机共振现象; 而且调节非线性项参数时, 随机共振效果随α稳定噪声的指数的减小而减弱, 但当调节线性项参数时, 随机共振效果则随着α稳定噪声的特征指数的减小而增强. 本文的结论在α稳定噪声环境下, 利用参数诱导随机共振原理进行弱信号检测方面具有重要的理论意义, 并有助于理解不同α稳定噪声对一般随机共振系统的共振效果的影响.     

二值噪声激励下欠阻尼周期势系统的随机共振

研究了二值噪声和周期信号共同激励下欠阻尼周期势系统的随机共振. 利用随机能量法计算了系统的平均输入能量和平均输出信号的振幅和相位差, 讨论了二值噪声对随机共振的影响. 发现随着噪声强度的增大, 平均输入能量曲线存在一个极小值和一个极大值, 系统出现先抑制后共振的现象; 同时, 系统信噪比曲线随噪声强度的增加出现单峰现象, 说明系统存在随机共振现象.     

Duffing系统随机相位抑制混沌与随机共振并存现象的机理研究

针对随机相位作用的Duffing混沌系统, 研究了随机相位强度变化时系统混沌动力学的演化行为及伴随的随机共振现象. 结合Lyapunov指数、庞加莱截面、相图、时间历程图、功率谱等工具, 发现当噪声强度增大时, 系统存在从混沌状态转化为有序状态的过程, 即存在噪声抑制混沌的现象, 且在这一过程中, 系统亦存在随机共振现象, 而且随机共振曲线上最优的噪声强度恰为噪声抑制混沌的参数临界点. 通过含随机相位周期力的平均效应分析并结合系统的分岔图, 探讨了噪声对混沌运动演化的作用机理, 解释了在此过程中随机共振的形成机理, 论证了噪声抑制混沌与随机共振的相互关系.     

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     

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     

一类线性阻尼振子的随机共振研究

针对随机有色噪声参数激励和周期调制噪声外激励联合作用下的线性阻尼振子,利用Shapiro-Loginov公式推导了系统响应的一、二阶稳态矩的解析表达式.发现这类系统存在传统的随机共振、广义的随机共振和“真正”的随机共振;当乘性噪声强度和调制噪声强度的比值大于等于1时,系统出现随机多共振现象.通过数值计算的系统响应功率谱,验证了理论分析结果. 关键词： 随机共振 周期调制的噪声 线性阻尼振子     

α稳定噪声驱动的非对称双稳随机共振现象

以微弱周期信号激励的非对称双稳系统为模型,以信噪比增益为指标,首先针对加性和乘性α稳定噪声共同作用的随机共振现象展开了研究,然后针对单独加性α稳定噪声激励的随机共振现象进行了研究,探究了α稳定噪声特征指数α和对称参数β分别取不同值时,系统结构参数a,b,刻画双稳系统非对称性的偏度r以及α稳定噪声强度放大系数Q或D对非对称双稳系统共振输出的作用规律.研究结果表明,无论在加性和乘性α稳定噪声共同作用下还是在单独加性α稳定噪声作用下,通过调节a和b或者r均可诱导随机共振,实现微弱信号的检测,且有多个参数区间与之对应,这些区间不随α或β的变化而变化;在研究噪声诱导的随机共振现象时发现,调节噪声强度放大系数也可使系统产生随机共振现象,且达到共振状态时D的区间也不随α或β的变化而变化.这些结论为α稳定噪声环境下参数诱导随机共振中系统参数以及噪声诱导随机共振中噪声强度的合理选取提供了依据.     

一类非线性神经网络中噪声改善信息传输

以互信息为测度,通过数值计算和计算机仿真比较详细地讨论了在加性和乘性噪声共同作用下的一类非线性神经网络中噪声改善信息传输的(阈上)随机共振现象.在一定的系统阈值和固定的乘性(或加性)噪声强度下,互信息随着加性(或乘性)噪声强度的增加显示出上凸变化,(阈上)随机共振出现;系统阈值单元数目的增加可增强信息传输的效果;系统阈值的增加使得信号处在阈下的成分增多,(阈上)随机共振现象更容易发生.另外,改变加性噪声强度比改变乘性强度时(阈上)随机共振更容易发生.以上结果说明(阈上)随机共振现象的存在性和噪声改善信息传输的效果与乘性或加性噪声强度、阈值单元数以及系统阈值水平密切相关.     

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     

Stochastic resonance in a monostable system driven by square-wave signal and dichotomous noise

<正>This paper investigates the stochastic resonance in a monostable system driven by square-wave signal,asymmetric dichotomous noise as well as by multiplicative and additive white noise.By the use of the properties of the dichotomous noise,it obtains the expressions of the signal-to-noise ratio under the adiabatic approximation condition.It finds that the signal-to-noise ratio is a non-monotonic function of the asymmetry of the dichotomous noise,and which varies non-monotonously with the intensity of the multiplicative and additive noise as well as the system parameters.Moreover, the signal-to-noise ratio depends on the correlation rate and intensity of the dichotomous noise.     

Analysis of weak signal detection based on tri-stable system under Levy noise

Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resonance system.The average signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon.The characteristics of tri-stable stochastic resonance under Levy noise is analyzed in depth.First,the method of generating Levy noise,the effect of tri-stable system parameters on the potential function and corresponding potential force are presented in detail.Then,the effects of tri-stable system parameters w,a,b,and Levy noise intensity amplification factor D on the resonant output can be explored with different Levy noises.Finally,the tri-stable stochastic resonance system is applied to the bearing fault detection.Simulation results show that the stochastic resonance phenomenon can be induced by tuning the system parameters w,a,and b under different distributions of Levy noise,then the weak signal can be detected.The parameter intervals which can induce stochastic resonances are approximately equal.Moreover,by adjusting the intensity amplification factor D of Levy noise,the stochastic resonances can happen similarly.In bearing fault detection,the detection effect of the tri-stable stochastic resonance system is superior to the bistable stochastic resonance system.     

随机共振控制的频率匹配方法

根据非线性双稳系统在噪声和弱周期信号作用下产生随机共振的随机同步条件，提出了随机共振控制的频率匹配方法.理论分析和数值仿真结果表明，随机共振是可控制的，通过控制输入信号的频率和噪声的统计特性，不仅能拓宽产生随机共振的频率范围，而且能增强共振的强度，从而实现有更多的噪声能量转换为信号能量. 关键词： 随机共振 非线性双稳系统 频率匹配 控制     

具有固有频率涨落的记忆阻尼线性系统的随机共振

研究了在内噪声、外噪声(固有频率涨落噪声)及周期激励信号共同作用下具有指数型记忆阻尼的广义Langevin方程的共振行为.首先将其转化为等价的三维马尔可夫线性系统,再利用Shapiro-Loginov公式和Laplace变换导出系统响应一阶矩和稳态响应振幅的解析表达式.研究发现,当系统参数满足Routh-Hurwitz稳定条件时,稳态响应振幅随周期激励信号频率、记忆阻尼及外噪声参数的变化存在"真正"随机共振、传统随机共振和广义随机共振,且随机共振随着系统记忆时间的增加而减弱.数值模拟计算结果表明系统响应功率谱与理论结果相符.     

Stochastic resonance in a single-mode laser driven by quadratic pump noise and amplitude-modulated signal

This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by quadratic pump noise and amplitude-modulated signal. A new linear approximation approach is advanced to calculate the signal-to-noise ratio. In the linear approximation only the drift term is linearized, the multiplicative noise term is unchangeable. It is found that there appears not only the standard form of stochastic resonance but also the broad sense of stochastic resonance, especially stochastic multiresonance appears in the curve of signal-to-noise ratio as a function of coupling strength λ between the real and imaginary parts of the pump noise.     

A study of stochastic resonance in a bistable system with double stochasticity

In a simple stochastic system—an overdamped Kramers oscillator with two noise sources (sources of white and dichotomic noise)—stochastic resonance is investigated theoretically and by means of analog simulation as a function of the asymmetry of the potential and the amplitude and the correlation time of the dichotomic noise. It is found that stochastic resonance is observed under slow (compared with the Kramers switching time) dichotomic noise and the signal-to-noise ratio (SNR) has a maximum for a noise amplitude equal to static bias.     

Stochastic resonance at phase noise in signal transmission

A model is developed for a periodic signal corrupted by an arbitrarily distributed phase noise and transmitted by an arbitrary memoryless system. The model establishes a new form of the phenomenon of stochastic resonance, whereby signal transmission can be enhanced by addition of noise. This is revealed by the standard signal-to-noise ratio of stochastic resonance, which here receives an explicit theoretical expression, and which is shown improvable via noise addition. This model is the first to propose a theory of stochastic resonance with phase noise. It represents a unique framework for further investigations on stochastic resonance and its applications.     

Intrinsic noise induced resonance in presence of sub-threshold signal in Brusselator

In a system of non-linear chemical reactions called the Brusselator, we show that intrinsic noise can be regulated to drive it to exhibit resonance in the presence of a sub-threshold signal. The phenomena of periodic stochastic resonance and aperiodic stochastic resonance, hitherto studied mostly with extrinsic noise, is demonstrated here to occur with inherent systemic noise using exact stochastic simulation algorithm due to Gillespie. The role of intrinsic noise in a couple of other phenomena is also discussed.     

基于随机共振进行弱信号探测的实验研究

非线性随机共振系统可利用噪声增强微弱信号检测的能力,为强噪声背景下微弱信号的检测开创了新方法.基于随机共振的基本原理设计了硬件电路系统,并将其应用于检测单频和多频微弱信号;通过输入模拟工程实际的带噪信号,采样所得的输出信号的频谱分析结果表明,利用随机共振技术可从强噪声背景下有效地提取出单频和多频弱信号.多频弱信号的有效提取拓展了基于随机共振原理的弱信号检测技术的应用领域,结合数字滤波处理技术有效地消除了低频噪声对信号识别的影响.基于随机共振的弱信号检测技术在信息识别与信息处理方面具有巨大的潜在的应用价值.