非高斯噪声激励下FitzHugh-Nagumo神经元系统的随机共振

研究了乘性非高斯噪声和加性高斯白噪声共同激励下FitzHugh-Nagumo(FHN) 神经元系统的随机共振问题. 利用路径积分法和两态模型理论, 推导出系统信噪比的表达式. 研究结果表明: 系统参数在不同的取值条件下, FHN神经元模型出现了随机共振和双重随机共振现象. 此外, 非高斯参数q在不同的取值条件下, 乘性噪声强度和加性噪声强度对信噪比的影响是不同的. 非高斯噪声的加入有利于增强FHN神经元系统的信号响应.     

关联高斯与非高斯噪声激励的FHN神经元系统的稳态分析

本文主要研究了关联乘性非高斯噪声和加性高斯白噪声共同激励的FHN(Fitz Hugh-Nagumo)神经元系统.利用路径积分法和统一色噪声近似,推导出该系统的定态概率密度函数表达式.通过研究发现,乘性噪声强度D、加性噪声强度Q、噪声自关联时间τ以及互关联系数λ均可以诱导系统产生非平衡相变现象,而非高斯参数q却不可以诱导系统产生非平衡相变现象.此外,我们还发现参数D和λ的增大有利于神经元系统从激发态向静息态转换,Q和τ的增大有利于神经元系统从静息态向激发态转换,q的增大会使得神经元系统停留在静息态的概率增加.     

非高斯噪声激励下FHN神经元系统的定态概率密度与平均首次穿越时间

研究了非高斯噪声激励下的FHN神经元系统,应用路径积分法和统一色噪声近似得到系统的定态概率密度函数和平均首次穿越时间表达式.发现了加性噪声强度Q能够诱导非平衡相变的产生,乘性噪声强度D、偏离参数p及关联时间τ₀均不能诱导非平衡相变发生;非高斯噪声的存在缩短了细胞神经元系统静息态和激发态之间的转化时间,有利于神经元信息的传递. 关键词： FHN神经元系统 非高斯噪声 定态概率密度 平均首次穿越时间     

二维映射神经元模型中频率依赖的随机共振

通过数值模拟方法, 研究了在具有稳定次阈值振荡特性的二维映射神经元体系中, 噪声对体系非线性动力学的调控作用. 通过计算发现了噪声诱导的动作电位和随机共振现象. 另外,还研究了体系的控制参数及输入信号的频率对体系动力学的影响, 发现了该体系中频率依赖的随机共振现象. 关键词： 二维映射神经元模型 次阈值振荡 高斯白噪声 随机共振     

高斯白噪声对神经元二维映射模型动力学的影响

从神经元二维映射模型出发，用高斯白噪声模拟了神经元的噪声环境，进而研究了高斯白噪声对参数空间相图的影响.研究发现，噪声可以提高系统的可兴奋性.通过数值模拟研究了噪声引起的相干共振现象.结果表明，只有当系统参数选取在静息区域且接近连续点火和静息状态分界线时才可以得到相干共振现象. 关键词： 高斯白噪声 神经元二维映射模型 相图 相干共振     

非高斯噪声驱动下一维双稳系统的逻辑操作

本文以成功率作为逻辑随机共振的测度, 主要研究了非高斯噪声激励下一维双稳系统的逻辑随机共振现象, 并用平均首次通过时间的方法对此现象的机理进行了解释. 研究结果表明: 只有在适当的噪声强度带或关联时间带上, 成功率才会达到共振峰值. 通过对系统参数进行优化, 提高了系统实现逻辑操作的可靠性. 关键词： 逻辑随机共振 一维双稳系统 非高斯噪声 平均首次通过时间     

非高斯噪声驱动下非对称双稳系统的平均首次穿越时间与随机共振研究

研究了乘性非高斯噪声和加性高斯白噪声共同激励下非对称双稳系统的平均首次穿越时间和随机共振问题. 利用路径积分法和两态模型理论,推导出平均首次穿越时间和信噪比的表达式. 研究结果表明:势阱非对称性对两个不同方向的平均首次穿越时间的影响是不同的. 信噪比是加性噪声强度和势阱非对称性的非单调函数,系统出现了随机共振现象;信噪比是乘性噪声强度的单调函数,没有共振峰出现. 这说明该系统中乘性噪声强度和加性噪声强度对信噪比的影响是不同的. 关键词： 非高斯噪声 非对称双稳系统 平均首次穿越时间 随机共振     

非磁化等离子体Hopf分岔处随机共振实验

在非磁化的直流放电等离子体中,利用系统内禀的周期驱动力与外加的高斯白噪声的协同作用,成功地在系统动力学轨道Hopf分岔的不动点一侧,观察到了周期信号的信噪比被噪声改善的随机共振现象.一维过阻尼系统的随机共振模型可以解释所观察的实验结果.比较实验结果与理论模型可知,系统动力学轨道发生Hopf分岔的原因是系统双稳态之间势垒的变化 在Hopf分岔的极限环一侧观察不到随机共振现象,其原因是此时系统已经处于超阈值周期驱动的状态     

双稳动力学系统中耦合效应对逻辑随机共振现象的增强作用

研究了电路耦合作用对逻辑随机共振现象以及逻辑门器件稳定性的影响．相对于单个的逻辑门电路,耦合的逻辑门器件可以在更宽的噪声范围内都保持逻辑运算的准确性,即耦合作用可以增强逻辑随机共振现象．此外,这种增强效应随着耦合体系尺度的增大而增大,但是当体系尺度达到一定程度时,这种增强作用达到一个稳定值．最后还考察了耦合强度的影响,发现随着耦合强度的增加,逻辑门器件可以保持逻辑运算准确性所对应的噪声区间非单调地改变,表现出一种共振的行为.     

非磁化等离子本Hopf分岔处随机共振实验

在非磁化的直流放电等离子本中,利用系统内禀的周期驱动力与外加的高斯白噪声的协同作用,成功地在系统动力学轨道Ｈｏｐｆ分岔的不动点一侧,观察到了周期信号的信噪比被噪声改善的随机共振现象。一维过阻尼系统的随机共振模型可以解释反观察的实验结果。比较实验实验结果与理论模型可知,系统动力学轨道发生Ｈｏｐｆ分岔的原因是系统双稳态之间势垒的变化;在Ｈｏｐｆ分岔的极限环一侧观察不到随机共振现象,其原因是此时系统已经     

Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise

We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of colored noise and a periodic signal. Two cases are considered: (i) the dynamics of the membrane potential is affected by the noise, (ii) the slow dynamics of the recovery variable is subject to noise. We investigate the role of the colored noise on the neuron dynamics by the mean response time (MRT) of the neuron. We find meaningful modifications of the resonant activation (RA) and noise enhanced stability (NES) phenomena due to the correlation time of the noise. For strongly correlated noise we observe suppression of NES effect and persistence of RA phenomenon, with an efficiency enhancement of the neuronal response. Finally we show that the self-correlation of the colored noise causes a reduction of the effective noise intensity, which appears as a rescaling of the fluctuations affecting the FHN system.     

Enhancement of stability in randomly switching potential with metastable state

The overdamped motion of a Brownian particle in randomly switching piece-wise metastable linear potential shows noise enhanced stability (NES): the noise stabilizes the metastable system and the system remains in this state for a longer time than in the absence of white noise. The mean first passage time (MFPT) has a maximum at a finite value of white noise intensity. The analytical expression of MFPT in terms of the white noise intensity, the parameters of the potential barrier, and of the dichotomous noise is derived. The conditions for the NES phenomenon and the parameter region where the effect can be observed are obtained. The mean first passage time behaviors as a function of the mean flipping rate of the potential for unstable and metastable initial configurations are also analyzed. We observe the resonant activation phenomenon for initial metastable configuration of the potential profile.Received: 16 June 2004, Published online: 31 August 2004PACS: 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 02.50.-r Probability theory, stochastic processes, and statistics - 05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)     

Role of noise in a market model with stochastic volatility

We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES effect in our model with stochastic volatility. We investigate the role of the correlation between the two noise sources on the NES effect.     

Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction

The role of thermal and non-Gaussian noise on the dynamics of driven short overdamped Josephson junctions is studied. The mean escape time of the junction is investigated considering Gaussian, Cauchy-Lorentz and Lévy-Smirnov probability distributions of the noise signals. In these conditions we find resonant activation and the first evidence of noise enhanced stability in a metastable system in the presence of Lévy noise. For Cauchy-Lorentz noise source, trapping phenomena and power law dependence on the noise intensity are observed.     

Effects of non-Gaussian noise near supercritical Hopf bifurcation

We have studied the effects of non-Gaussian colored noise in a chemical oscillation system, the well-known Brusselator model, in the parameter region close to the supercritical Hopf bifurcation. With the variation of the parameter q, which quantifies the deviation from Gaussian character, the signal-to-noise ratio of noise induced oscillation exhibits a bell-shaped change, indicating the presence of resonant activity. The cooperative effects of q and the correlation time τ on the performance of noise induced oscillation are also investigated. Interestingly, resonance-like behavior can be induced by either q or τ when the other parameter is properly fixed. Stochastic normal form theory is used to analyze these nontrivial effects and the simulation results are well reproduced. This work provides us comprehensive understanding of how non-Gaussian noise influences the dynamics in chemical oscillation systems.     

Effects of non-Gaussian noise on a calcium oscillation system

We investigate the effects of the non-Gaussian colored noise on a calcium oscillation system using stochastic simulation methods. It is found that the reciprocal coefficient of variance R has a maximum (R max ) with increasing noise intensity Q. The non-Gaussian noise parameter q has an important effect on the system. For some values of q (e.g., q = 0.9, q = 1.0), R has a maximum with increasing correlation time τ. Non-Gaussian noise induced spikes are more regular than Gaussian noise induced spikes when q is small and Q has large values. The R has a maximum with increasing q. Therefore, non-Gaussian noise could play more effective roles in the calcium oscillation system.     

Controlling the noise enhanced stability effect via noise recycling in a metastable system

We analyze the role of the delay time τ _d and the fraction ε of recycled noise on the enhancement of the mean first-passage time (MFPT) in a metastable system with recycled noise, generated by the superposition of a primary Gaussian noise source with a second component of constant delay. The results indicate that MFPT as a function of the noise intensity D shows either a non-monotonic behavior with a maximum or a divergent behavior, which is the identifying characteristic of the noise enhanced stability (NES) phenomenon. The increasing of τ _d or ε strengthens the NES effect for ε > 0. However, for ε < 0, there is a critical value of τ _d , below which we observe an increase of MFPT whose maximum goes to infinity, and above which the divergent behavior tends to disappear and MFPT versus D shows a transition from one peak to two peaks and eventually one peak as τ _d or |ε| increases. Moreover, we also discuss the effect of different initial conditions. These observations illustrate that the noise recycling may be used as an effective scheme for controlling the NES effect.     

Ballistic diffusion induced by non-Gaussian noise

In this letter,we have analyzed the diffusive behavior of a Brownian particle subject to both internal Gaussian thermal and external non-Gaussian noise sources.We discuss two time correlation functions C(t) of the non-Gaussian stochastic process,and find that they depend on the parameter q,indicating the departure of the non-Gaussian noise from Gaussian behavior:for q ≤ 1,C(t) is fitted very well by the first-order exponentially decaying curve and approaches zero in the longtime limit,whereas for q 1,C(t) can be approximated by a second-order exponentially decaying function and converges to a non-zero constant.Due to the properties of C(t),the particle exhibits a normal diffusion for q ≤ 1,while for q 1 the non-Gaussian noise induces a ballistic diffusion,i.e.,the long-time mean square displacement of the free particle reads [x(t)-x(t)]2∝t2.     

Effect of time delay in FitzHugh-Nagumo neural model with correlations between multiplicative and additive noises

We study the effect of time delay in the FitzHugh-Nagumo neural model with correlations between multiplicative and additive noise terms. Based on the corresponding Fokker-Planck equation, the explicit expressions of the stationary probability distribution function (SPDF), the mean first passage time (MFPT) and the signal-to-noise ratio (SNR) are obtained, respectively. Research results show that: (i) the system undergoes a succession of two phase transitions (i.e., the reentrance phenomenon) as the noise correlation parameter is increased and a (single) phase transition as the time delay is increased. (ii) The MFPT as a function of the multiplicative noise intensity exhibits a maximum. This maximum for MFPT identifies the noise enhanced stability (NES) effect, the noise correlation parameter intensifies the NES effect while the time delay, and the additive noise intensity weakens it. (iii) The existence of a maximum in the SNR as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance (SR) phenomenon, the noise correlation parameter enhances the SR while the time delay, and the additive noise intensity weaken it.     

Escape process and stochastic resonance under noise intensity fluctuation

We study the effects of noise intensity fluctuations on the stationary and dynamical properties of an overdamped Langevin model with a bistable potential and external periodical driving force. We calculated the stationary distributions, mean-first passage time (MFPT) and the spectral amplification factor using a complete set expansion (CSE) technique. We found resonant activation (RA) and stochastic resonance (SR) phenomena in the system under investigation. Moreover, the strength of RA and SR phenomena exhibit non-monotonic behavior and their trade-off relation as a function of the squared variation coefficient of the noise intensity process. The reliability of CSE is verified with Monte Carlo simulations.