Could one single dichotomous noise cause resonant activation for exit time over potential barrier？

This paper studies the mean first passage time （or exit time, or escape time） over the non-fluctuating potential harrier for a system driven only by a dichotomous noise. It finds that the dichotomous noise can make the particles escape over the potential barrier, in some circumstances; but in other circumstances, it can not. In the case that the particles escape over the potential harrier, a resonant activation phenomenon for the mean first passage time over the potential barrier is obtained.     

Noise-intensity fluctuation in Langevin model and its higher-order Fokker-Planck equation

In this paper, we investigate a Langevin model subjected to stochastic intensity noise (SIN), which incorporates temporal fluctuations in noise-intensity. We derive a higher-order Fokker-Planck equation (HFPE) of the system, taking into account the effect of SIN by the adiabatic elimination technique. Stationary distributions of the HFPE are calculated by using the perturbation expansion. We investigate the effect of SIN in three cases: (a) parabolic and quartic bistable potentials with additive noise, (b) a quartic potential with multiplicative noise, and (c) a stochastic gene expression model. We find that the existence of noise-intensity fluctuations induces an intriguing phenomenon of a bimodal-to-trimodal transition in probability distributions. These results are validated with Monte Carlo simulations.     

Escape of Brownian particles and stochastic resonance with low-temperature quantum fluctuations

In this paper, we investigate the escape of Brownian particles and stochastic resonance (SR) with low-temperatures quantum fluctuations by using the quantum Smoluchowski equations at low-temperature. Two specific examples have been considered: one is the example of bistable system, and the other is the example of metastable system. The explicit expressions of the mean-first passage time (MFPT) and signal-to-noise ratio (SNR) for both specific examples are obtained, respectively. Based on the numerical compu...     

Suprathreshold stochastic resonance induced by ion channel fluctuation

In this study, we examine the signal detection ability of an array of neurons with intrinsic channel fluctuation. Numerical simulations show that estimation of the input signal from the output spiking activity of the neuronal array is most accurate if a proper amount of channel noise exists. Theoretical calculation of the mutual and Fisher information confirms the effect of the noise-aided information transfer in the array, or the presence of suprathreshold stochastic resonance. These results indicate that the channel noise, which induces response variability, may play an essential role in population coding.     

Monte Carlo simulation of overdamped motion in a double well potential under the influence of coloured noise

We present a Monte Carlo simulation algorithm for evaluating the stationary probability and the mean and the variance of first passage times in any dynamical system under the influence of additive coloured Gaussian and Marcovian noise (Ornstein-Uhlenbeck process). Our algorithm generates the Ornstein-Uhlenbeck process by a superposition of a finite number of random telegraph processes. We obtain our results from a direct evaluation of the trajectories. We apply our method to the overdamped motion of a particle in a double well potential. We compare our simulation results with various analytic approximations for the stationary probability and the mean first passage times.     

Coherence resonance and stochastic resonance in directionally coupled rings

In coupled systems, symmetry plays an important role for the collective dynamics. We investigate the dynamical response to noise with and without weak periodic modulation for two classes of ring systems. Each ring system consists of unidirectionally coupled bistable elements but in one class, the number of elements is even while in the other class the number is odd. Consequently, the rings without forcing show at a certain coupling strength, either ordering (similar to anti-ferromagnetic chains) or auto-oscillations. Analysing the bifurcations and fixed points of the two ring classes enables us to explain the dynamical response measured to noise and weak modulation. Moreover, by analysing a simplified model, we demonstrate that the response is universal for systems having a directional component in their stochastic dynamics in phase space around the origin.     

Stochastic resonance characteristic analysis of new potential function under Levy noise and bearing fault detection

Based on the output saturation of classcial bistable stochastic resonance (CBSR), a new type of piecewise nonlinear bistable stochastic resonance (PNBSR) system is constructed. The mean signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon. The laws for the resonant output of piecewise nonlinear bistable system governed by l, c, a, b and D of Levy noise are explored under different characteristic index α and symmetry parameter β of Levy noise. The results show that the output of PNBSR system has increased 4?dB by comparing with the output signal-to-noise ratio of CBSR system. And the stochastic resonance phenomenon can be induced by adjusting the piecewise nonlinear system's parameters under any α or β of Levy noise. The interval of the parameters of system which induces good stochastic resonance is roughly the same. And the output signal waveform of resonance is very similar to the input signal waveform, which has some reference value for the signal recovery. Moreover, we can find the good stochastic resonance interval of the system parameters do not change with D of Levy noise under the different noise intensity D of Levy noise. On the basis of this, adjusting the intensity amplification factor D of Levy noise, which induces good stochastic resonance, and the interval does not change with α or β. At last, the piecewise nonlinear bistable system is applied to detect bearing fault signals, which achieves better performance compared with the classical bistable system.     

Chaos and reverse transitions in stochastic resonance

Stochastic resonance is a phenomenon that a weak signal can be amplified and optimized by the assistance of noise in bistable system. There is still not enough research on the mutual interplay among system, noise and signal. In this paper, we study the role of every parameter in nonlinear transfer and discover chaos phenomenon in stochastic resonance. To measure the influence of chaos, a trajectory decision function was proposed. Based on this function, we found two forms of stochastic resonance, clockwise resonance and counterclockwise resonance.     

I/f noise in systems showing stochastic resonance

Stochastic resonator systems with input and/or output 1/f noise have been studied. Disordered magnets/dielectrics serve as examples for the case of output 1/f noise with white noise (thermal excitation) at the input of the resonators. Due to the fluctuation-dissipation theorem, the output noise is related to the out-of-phase component of the periodic peak of the output spectrum. Spin glasses and ferromagnets serve as interesting examples of coupled stochastic resonators. A proper coupling can lead to an extremely large signal-to-noise ratio. As a model system, a l/f-noise-driven Schmitt trigger has been investigated experimentally to study stochastic resonance with input 1/f noise. Under proper conditions, we have found several new nonlinearity effects, such as peaks at even harmonics, holes at even harmonics, and 1/f noise also in the output spectrum.     

噪声间关联程度的时间周期调制对单模激光随机共振的影响

用线性化近似的方法研究了噪声间关联程度λ受时间周期性调制的单模激光增益模型的光强功率谱及信噪比.具体讨论信噪比R受加法噪声强度D,乘法噪声强度Q及噪声间关联程度λ的影响,以及受周期调制频率Ω_λ,输入信号频率Ω的影响.发现了一些新颖的现象. 关键词： 时间周期调制频率 噪声间关联程度 随机共振 信噪比     

Long-term climatic transitions and stochastic resonance

Stochastic resonance constitutes one of the few plausible mechanisms capable of explaining the recurrent climatic changes that occurred on earth during the Quaternary era. In this paper early attempts and more recent progress to model these phenomena on a global scale are reviewed.     

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.     

Stochastic resonance, reverse-resonance and stochastic multi-resonance in an underdamped quartic double-well potential with noise and delay

The stochastic resonance in an underdamped quartic double-well potential with time delayed feedback is studied numerically. The signal power amplification is employed to characterize the stochastic resonance of the system. Simulation results indicate that: (i) for moderate frequency of the periodic driving, the stochastic resonance is decreased monotonically by increasing the delay time, but at high frequency, the reverse-resonance is induced to transform into a stochastic resonance by time delay; (ii) the damping coefficient has a critical value for which the stochastic resonance is optimum; (iii) a stochastic multi-resonance emerges when the signal power amplification is a function of the driving frequency.     

色噪声间关联的周期调制对单模激光随机共振的影响

讨论色噪声驱动的单模激光系统在噪声间关联程度受时间周期调制情况下的随机共振.用线性化近似的方法计算了光强功率谱及信噪比.具体讨论色噪声情况下信噪比R受噪声强度D,Q,时间周期调制频率Ω_λ以及噪声自关联时间τ₁,τ₂和噪声间关联程度λ的影响.发现信噪比随噪声强度的变化呈单峰共振,信噪比随时间周期调制频率的变化呈周期性共振,而信噪比随 关键词： 色噪声 时间周期调制 噪声间关联程度 周期性随机共振     

Impact of colored cross-correlated noises on stochastic resonance and mean extinction rate for a metapopulation system with a multiplicative periodic signal

In this paper, we aim to explore the mean extinction rate and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by a multiplicative periodic signal, colored cross-correlated multiplicative and additive Gaussian noises. By use of the fast descent method and the adiabatic approximation theory for the signal-to-noise ratio, we obtain the expression of the signal-to-noise ratio (SNR). Numerical results indicate that the various SR phenomena occur in the metapopulation system due to the variation of the noise terms and the correlation time. Specifically, the noise correlation always plays a critical role in motivating the SR phenomenon, while the multiplicative noise exerts the inhibition effect on the SR. Interestingly, the weak additive noise can stimulate the resonant peak of the SNR, while the further increase of the noise intensity will lead to the reduction of the SR effect. On the other hand, the noise correlation time τ plays antipodal roles in motivating the SR phenomenon under different circumstances. With regard to the mean extinction rate of the population from the boom state to the extinction one, by performing the numerical calculations, it is found that the additive noise always accelerate the extinction of the population, while the correlation noise will slow down the decline for the population. The role that the noise correlation time plays in the population extinction depends on the values that λ takes.     

Solutions of fractional nonlinear diffusion equation and first passage time: Influence of initial condition and diffusion coefficient

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with diffusion coefficient separable in time and space, D(t,x)=D(t)|x|^−θ, subject to absorbing boundary condition and the conventional initial condition p(x,0)=δ(x−x₀). We obtain explicit analytical expressions for the probability distribution, the first passage time distribution, the mean first passage time and the mean squared displacement, and discuss their behavior corresponding to different time dependent diffusion coefficients.     

Coherence and stochastic resonance in a delayed bistable system

Both coherence resonance (CR) and stochastic resonance (SR) in a delayed bistable system driven by additive and multiplicative white noises and a weak harmonic excitation are studied by using the theory of two-state model. For the weak noise intensity and delayed feedback, the analytic expressions of power-spectrum and linear-spectrum amplification are derived to quantify the CR and the SR, respectively. The study shows that the peak in the power spectrum at the frequency corresponding to the time delay attains the maximum for an appropriate amount of additive noise intensity and the CR manifests. The feedback gain plays an important role in the SR. For example, the positive feedback gain enhances the SR, but the negative feedback gain suppresses the system output and makes the SR disappear. Moreover, the system also exhibits the frequency SR.     

Self-tuning and stochastic resonance in a simple threshold system—a filter theory approach

Fully nonlinear filter theory is applied to a simple threshold system, which plays the role of an observer of input signals from a Brownian dynamical system. Our filtering results are discussed within the frameworks of both stochastic resonance and self-tuning of the threshold values, which gathers a lot of attention in relation to information processing in auditory systems.     

Experimental investigation of noise-assisted information transmission and storage via stochastic resonance

We present experimental results on the information transmission and storage via stochastic resonance in circuits designed and built around Schmitt triggers (STs). First, we investigate the performance of a transmission line comprised of five STs and show it to exhibit stochastic resonance. Each ST in the line is fed with white Gaussian noise, and the first ST is driven by a non-return-to-zero pseudo-random bit sequence with sub-threshold amplitude. Parameters such as bit error rate (Q-factor) are measured (calculated) and shown to exhibit a minimum (maximum) for an optimum amount of noise. Interestingly, we find that system performance degrades with the number of STs as if the system were linear and impaired only by additive Gaussian noise. We then propose and build a 1-bit storage device based on two STs in a loop configuration. We demonstrate that such a system is capable of storing one bit of information only in the presence of noise, and that there is a regime where the efficiency of such a device increases with increasing noise.Our results point to the feasibility of building ‘blocks’ that can transmit, store and eventually process information, whose performance is not only robust against noise, but can actually benefit from it.     

Linear response and stochastic resonance of superparamagnets

The standard mathematical expression for the response functions of the linear response theory for Markovian stochastic systems, constructed from the corresponding Fokker-Planck equation, is transformed into an expression which is very suitable for numerical simulations. The method is applied to a stochastic model for superparamagnetism presented previously by the authors. For convenient values of the parameters the model shows the phenomenon of stochastic resonance.