二值噪声驱动下二阶线性系统的随机共振

研究了二值噪声驱动下二阶线性系统的随机共振问题. 采用平均法推导出系统输出幅值增益的表达式,考察了幅值增益与系统频率、输入信号频率、噪声强度和噪声相关时间的关系,发现系统输出幅值增益随这些参量呈单峰共振变化. 另外,二值噪声的非对称性对共振峰值具有很大影响. 关键词： 随机共振 幅值增益 二值噪声 二阶线性系统     

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     

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     

色高斯噪声驱动双稳系统的多重随机共振研究

研究了由色关联乘性和加性色噪声作用下的双稳系统的随机共振问题,在绝热近似条件下得到了信噪比的表达式.通过分析所得的初始条件为 x(0)=x₊ 时的信噪比,发现了单随机共振和多重随机共振现象;分析了噪声强度、噪声关联时间和关联强度对系统信噪比的影响. 关键词： 多重随机共振 信噪比 双稳模型 色关联色噪声     

信号调制下色噪声间关联的周期调制对单模激光随机共振的影响

在色噪声间的关联程度受时间周期调制的激光系统中,研究噪声受信号调制情况下的随机共振.用线性化近似的方法计算了光强关联函数及信噪比.具体讨论信噪比随噪声强度、噪声自关联时间、信号频率以及时间周期调制频率的变化关系.发现一种新的随机共振：信噪比随时间周期调制频率的变化出现周期振荡型随机共振;发现广义随机共振：信噪比随抽运噪声自关联时间的变化、随信号频率的变化出现随机共振;同时也存在典型的信噪比随噪声强度的变化而出现的随机共振.而信噪比随量子噪声自关联时间的变化表现为抑制. 关键词： 信号调制 时间周期调制 噪声间关联程度 周期振荡型随机共振     

弱信号在Hodgkin-Huxley神经元单向耦合系统中的传输特性

研究了阈下信号在含噪声的Hodgkin-Huxley神经元单向耦合系统中的传输特性.结果表明,各单元中均存在随机共振现象,可见噪声有助于提高信号的检测和传输;另外,耦合实现了信号的传输,且随着耦合强度的增强信号的传输效率增加,在耦合强度达到某一程度时两神经元实现了有时延的一致放电;并且接收元的信噪比最优值处的噪声强度随着耦合强度的提高而减小,最终与驱动元的一致;另外在耦合强度过强时,接收元出现过耦合放电,但是最终会被不断增强的噪声抑制,此现象有助于解释神经元的自放电及神经系统的自调节.研究表明噪声和耦合在 关键词： Hodgkin-Huxley神经元模型 随机共振 噪声 单向耦合系统     

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     

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     

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.     

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.     

Collective firing regularity of a scale-free Hodgkin–Huxley neuronal network in response to a subthreshold signal

We consider a scale-free network of stochastic HH neurons driven by a subthreshold periodic stimulus and investigate how the collective spiking regularity or the collective temporal coherence changes with the stimulus frequency, the intrinsic noise (or the cell size), the network average degree and the coupling strength. We show that the best temporal coherence is obtained for a certain level of the intrinsic noise when the frequencies of the external stimulus and the subthreshold oscillations of the network elements match. We also find that the collective regularity exhibits a resonance-like behavior depending on both the coupling strength and the network average degree at the optimal values of the stimulus frequency and the cell size, indicating that the best temporal coherence also requires an optimal coupling strength and an optimal average degree of the connectivity.     

自催化三分子模型内噪声随机共振

运用化学Langevin方程 ,数值研究了内噪声对单个和单向耦合自催化三分子模型动力学行为的影响 .研究发现 ,对于单个振子体系 ,内噪声可以诱导持续振荡 ,而且随着系统尺度的增大 ,信噪比经过一个极大值 ,从而证明了内噪声随机共振和最佳尺度效应的存在 ;对于单向耦合系统 ,信噪比还随耦合强度的变化而经过极大值 .此外 ,边界条件对耦合体系的内噪声随机共振行为有很大影响 ,非零流条件下 ,耦合可以增强内噪声随机共振 ,而零流条件下 ,耦合会抑制随机共振 ;当耦合强度适宜时 ,每个振子发生随机共振时的尺度几乎相同 ,表明最佳体系尺度和耦合强度有助于体系达到最佳的化学反应状态 .     

神经系统中随机和混沌感知信号的联想记忆与分割

为了模拟人与动物感知信息的真实环境，以脉动神经元节点组成神经元网络，研究在随机刺激和混沌刺激等极端条件下的记忆模式存储与时间分割问题.研究表明：网络对于若干种模式的叠加输入，能够以一部分神经元同步发放的形式在时间域上分割出每一模式. 如果输入模式是缺损的，系统能够把它们恢复到原型，即具有联想记忆功能.通过调节耦合强度和噪声强度等参数使得网络在中等强度噪声达到最优的时间分割，与广泛讨论的随机共振现象一致. 关键词： 神经网络 空时模式 联想记忆 随机共振     

Collective temporal coherence for subthreshold signal encoding on a stochastic small-world Hodgkin-Huxley neuronal network

We study the collective temporal coherence of a small-world network of coupled stochastic Hodgkin-Huxley neurons. Previous reports have shown that network coherence in response to a subthreshold periodic stimulus, thus subthreshold signal encoding, is maximal for a specific range of the fraction of randomly added shortcuts relative to all possible shortcuts, p, added to an initially locally connected network. We investigated this behavior further as a function of channel noise, stimulus frequency and coupling strength. We show that temporal coherence peaks when the frequency of the external stimulus matches that of the intrinsic subthreshold oscillations. We also find that large values of the channel noise, corresponding to small cell sizes, increases coherence for optimal values of the stimulus frequency and the topology parameter p. For smaller values of the channel noise, thus larger cell sizes, network coherence becomes insensitive to these parameters. Finally, the degree of coupling between neurons in the network modulates the sensitivity of coherence to topology, such that for stronger coupling the peak coherence is achieved with fewer added short cuts.     

Noise induced resonance phenomena in coupled map lattices

We analyse different types of resonance phenomena that can occur in a coupled map lattice in the presence of noise with a subthreshold signal. The onsite dynamics considered here is different from previous such studies, namely, a bimodal cubic map capable of bistability in its dynamics. In addition to the resonance observed in the temporal iterates (the conventional stochastic resonance), we establish the possibility of resonance patterns in spatial sequences along the lattice, which we refer to as “Lattice Stochastic Resonance”. The characterising features of both are investigated in detail, under different types of signals with nearest neighbour coupling between lattice points. Possible practical applications are in signal detection, image processing and in communication networks.     

Enhancement and weakening of stochastic resonance for a coupled system

In the paper, we investigate the phenomenon of stochastic resonance of a system with finite locally coupled linear elements driven by multiplicative dichotomous noise and temporal periodic signal. It is shown that, for some suitably selected values of the parameters, with increasing the size of the system or the coupling among the nearest elements, the stochastic resonance phenomenon can be enhanced; while for some other suitably selected parameters' values, with the increase of the size or the coupling, the phenomenon of stochastic resonance can be weakened. Our results can provide some useful insights for the investigation of the stochastic resonance phenomenon of the systems with locally (or globally) coupled finite (or infinite) elements.     

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.     

Additive noise in noise-induced nonequilibrium transitions

We study different nonlinear systems which possess noise-induced nonequlibrium transitions and shed light on the role of additive noise in these effects. We find that the influence of additive noise can be very nontrivial: it can induce first- and second-order phase transitions, can change properties of on-off intermittency, or stabilize oscillations. For the Swift-Hohenberg coupling, that is a paradigm in the study of pattern formation, we show that additive noise can cause the formation of ordered spatial patterns in distributed systems. We show also the effect of doubly stochastic resonance, which differs from stochastic resonance, because the influence of noise is twofold: multiplicative noise and coupling induce a bistability of a system, and additive noise changes a response of this noise-induced structure to the periodic driving. Despite the close similarity, we point out several important distinctions between conventional stochastic resonance and doubly stochastic resonance. Finally, we discuss open questions and possible experimental implementations. (c) 2001 American Institute of Physics.     

Effect of noise on coupled chaotic systems

The effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by identical noise, show synchronization phenomena where chaotic trajectories exponentially converge towards a single noisy trajectory, independent of the initial conditions. In a random neural network, with infinite range coupling, chaos is suppressed due to noise and the system evolves towards a fixed point. Spatiotemporal stochastic resonance phenomenon has been observed in a square array of coupled threshold devices where a temporal characteristic of the system resonates at a given noise strength. In a chaotically evolving coupled map lattice with the logistic map as local dynamics and driven by identical noise at each site, we report that the number ofstructures (a structure is a group of neighbouring lattice sites for values of the variable follow which the certain predefined pattern) follows a power-law decay with the length of the structure. An interesting phenomenon, which we callstochastic coherence, is also reported in which the abundance and lifetimes of these structures show characteristic peaks at some intermediate noise strength.     

FitzHugh-Nagumo神经元网络的联想记忆与分割

以广泛讨论的Fitz Hugh-Nagumo神经元节点组成脉动神经元网络,从神经系统空时模式编码理论研究网络的记忆(或模式)存储与时间分割问题.给定一个输入模式,它是几种模式的叠加,网络能够以一部分神经元同步发放的形式一个接一个地分割出每一种模式.如果输入的模式有缺损,系统能够把它们恢复成原型,即神经网络的联想记忆功能.模拟需要调节耦合强度和噪声强度等参数使得网络在特定的参数值和中等强度噪声达到最优的时间分割,与广泛讨论的随机共振现象一致.