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.     

Stochastic resonance in periodic potentials

We have studied the motion of a particle in a periodic potential plus a bias, driven by a noise and a coherent forcing. The response (power spectrum) of the particle at the driving forcing frequency is considered for different values of the noise intensity and of the bias. It is shown via direct simulation that the response displays the phenomenon of stochastic resonance, although the phenomenology is somehow different from the one observed in the standard bistable system.     

Stochastic resonance in multidimensional periodic potential

We study the mobility and diffusion of an underdamped Brownian particle moving in a two-dimensional (2D) periodic potential which subjects to a thermal white noise and a weak external driving force. Both the signal power amplification and the diffusion rate are calculated via Langevin simulations. It is shown that the stochastic resonance (SR) can be observed in the two dimension, namely, the output quantities as functions of the temperature show a nonmonotonic behavior, however, the SR cannot be obtained in the one dimension (1D). In the 2D potential, the height of dynamical barrier is decreased effectively along the direction of transport if the curvature of the potential at the barrier is less than that at the local minima. This leads to the SR condition being obeyed, i.e., the Kramers frequency over the barrier roughly matches the frequency of external signal.     

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.     

周期性外力驱动的混沌摆

为了简单直观地呈现混沌现象,研制了受周期驱动力驱动的混沌摆实验系统. 实验系统由力学机构、采集机构和数据处理分析仪组成. 力学机构是受周期外力驱动的复摆;采集机构采用无触点角度传感器,通过串口通信实时将数据传输给计算机;数据处理分析仪用虚拟仪器平台LabVIEW软件编程实现. 该系统可实时显示反映混沌基本特征的角度时序图、角速度时序图和相图.     

Stochastic resonance in periodic potentials driven by colored noise

We studied the motion of an underdamped Brownian particle in a periodic potential subject to a harmonic excitation and a colored noise. The average input energy per period and the phase lag are calculated to quantify the phenomenon of stochastic resonance (SR). The numerical results show that most of the out-of-phase trajectories make a transition to the in-phase state as the temperature increases. And the colored noise delays the transitions between these two dynamical states. The each curve of the average input energy per period and the phase lag versus the temperature exist a mono peak and SR appears in this system. Moreover, the optimal temperature where the SR occurs becomes larger and the region of SR grows wider as the correlation time of colored noise increases.     

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.     

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.     

外周期力驱动的倒摆混沌运动演示仪

设计并制作了受周期外力驱动的倒摆演示实验装置．利用自主开发的软件可自动演示和记录摆球运动状态的时间序列并存储实验数据．通过改变摆长、驱动电压，观察到该系统存在通过倍周期分岔通向混沌的过程．     

Brownian motion in periodic potentials; nonlinear response to an external force

The Brownian motion of particles in a periodic potential in response to a constant external force is investigated. By expanding the distribution function into Hermite-functions and into a Fourier-series, the Fokker-Planck-equation is transformed into a set of coupled equations for the expansion coefficients. These equations are solved by a continued fraction method for matrices. This continued fraction for the matrices converges for large, intermediate and even for very small damping constants. The mobility, the kinetic and potential energy for various damping constants and external forces are given for a cos-potential. The current-voltagecharacteristic of the Josephson tunneling junction is also shown.     

Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving

We study the phenomenon of stochastic resonance on Newman-Watts small-world networks consisting of biophysically realistic Hodgkin-Huxley neurons with a tunable intensity of intrinsic noise via voltage-gated ion channels embedded in neuronal membranes. Importantly thereby, the subthreshold periodic driving is introduced to a single neuron of the network, thus acting as a pacemaker trying to impose its rhythm on the whole ensemble. We show that there exists an optimal intensity of intrinsic ion channel noise by which the outreach of the pacemaker extends optimally across the whole network. This stochastic resonance phenomenon can be further amplified via fine-tuning of the small-world network structure, and depends significantly also on the coupling strength among neurons and the driving frequency of the pacemaker. In particular, we demonstrate that the noise-induced transmission of weak localized rhythmic activity peaks when the pacemaker frequency matches the intrinsic frequency of subthreshold oscillations. The implications of our findings for weak signal detection and information propagation across neural networks are discussed.     

Stochastic resonance in time-delayed exponential monostable system driven by weak periodic signals

Based on the exponential monostable potential, we study an exponential monostable system with time-delayed feedback driven by weak periodic signals and additive Gaussian white noises. The small delay approximation is used to deduce the steady-state probability distribution and the effective potential function is derived. The system parameters l and b, time delay τ, feedback strength β can change the shapes of the potential function. The mean first-passage time (MFPT) is calculated, which plays an extremely important role in the research of particles escape. And the signal-to-noise ratio (SNR) of the system can be obtained by using the adiabatic approximation theory. The phenomenon of stochastic resonance is investigated under different system parameters and time-delayed feedback. The amplitude of SNR can be changed by adjusting the system parameters. When the feedback strength β is positive (or negative), the time delay τ can promote (or suppress) the stochastic resonance phenomenon. The SNR versus the noise intensity D presents the stochastic resonance phenomenon. In addition, the SNR increases non-monotonically with the increasing feedback strength β and the parameter b. Also, the analysis and numerical simulation results of SNR are in good agreement with the formula simulation.     

Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal

This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker--Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity $Q$, multiplicative noise intensity $D$, static asymmetry $r$ and delay time $\tau$ on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry $r$ can restrain stochastic resonance, and the delay time $\tau $ can enhance stochastic resonance. Moreover, the longer the delay time $\tau $ is, the larger the additive noise intensity $Q$ and the multiplicative noise intensity $D$ are, when the stochastic resonance appears.     

随机外磁场作用下Ising自旋体系的随机共振

通过采用数字仿真手段，研究了经平均场处理的Ising自旋体系在弱确定性周期外场和随机外场（噪声场）混合驱动下的动态响应行为.着重考察了不同强度混合驱动外场作用下，Is ing自旋体系的非平衡动态转变所表现出区别于单纯确定性周期场作用下的新特征——随机 共振.选定体系非平衡动态转变的动态序参量Q为表征参量，系统模拟计算了混合驱动外场在多种参数组合下体系的动态响应特征，高场低温下的非连续动态转变和低场高温下的连续动态转变.模拟计算表明在适当混合驱动外场的作用下，Ising自旋体系具有随机共振现象，并诱发形成非 关键词： Ising自旋体系 随机共振 动态相变 对称性     

周期矩形信号作用下时滞非对称单稳系统 的随机共振

研究了周期矩形信号对时滞非对称单稳系统随机共振的影响,系统中加入的噪声均为Gauss白噪声.得到了信噪比的解析表达式,通过分析信噪比曲线发现系统存在随机共振现象.数值结果还表明乘性与加性噪声强度对信噪比的影响是不同的,在SNR-D参数平面上共振与抑制共存.在信噪比随着时滞量变化的曲线图上发现,当系统的非对称性|r|取值很大或者乘性与加性噪声强度比D/α小于1时,参数平面上的随机共振现象会消失.     

外力驱动下耦合弹簧振子的法诺共振

法诺共振是物理体系中普遍存在的一种非对称共振现象,它最早起源于量子物理,其微观图像是原子谱线中窄的分离态与宽的连续态之间的相干干涉.本文利用经典力学体系中两个弹簧振子的耦合,使其中一个弹簧振子受到周期性外力的驱动,成功类比了量子力学中的法诺共振现象.通过分析每个弹簧振子的动力学方程,严格求解它们的振动公式,从而得到每个...     

Stochastic resonance induced by bounded noise and periodic signal in an asymmetric bistable system

Stochastic resonance (SR) induced by the bounded noise in an asymmetric bistable system is investigated. Based on stochastic simulation, the signal power amplification SPA$SPA$ is derived for the case of the additive modulated signal. The simulation results indicate that: (1) the SR phenomenon is weakened by the asymmetry of the system; (2) increasing the frequency ω$\omega$ restricts the SR of the system; (3) there is an optimum value of amplitude A$A$ matching the strongest 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.     

Brownian motion in periodic potentials in the low-friction-limit; nonlinear response to an external force

The Brownian motion of particles in a periodic potential in response to a constant external force is investigated in the low-friction-limit. By introducing an energy and a space variable and by making a proper self consistent ansatz, the Fokker-Planck equation is solved in the stationary state for small friction constants. We found out that, for fixed force to friction ratios, the mobility times the friction constant is a linear function of the square root of the friction constant if the damping is small enough. Explicit results for this linear function are presented for a cosine potential and compared to previous results.     

具有频率涨落的简谐力激励下线性谐振子的随机共振

针对线性谐振子受到具有频率涨落的简谐力激励的情况, 计算出系统响应的一阶矩解析表达式.研究发现系统的输出响应以固有频率振动, 响应振幅随简谐激励力频率的变化出现"真实"随机共振,随固有频率的变化出现抑制和 共振两种现象.