小世界神经元网络随机共振现象:混合突触和部分时滞的影响

实际神经元网络中,信息传递时电突触和化学突触同时存在,并且有些神经元间的时滞很小可以忽略.本文构建了带有不同类型突触耦合的小世界网络,研究部分时滞、混合突触及噪声对随机共振的影响.结果表明:兴奋性和抑制性突触的比例影响共振的产生;在抑制性突触为主的网络里,几乎不产生随机共振.系统最佳噪声强度和化学突触比例大致呈线性递增关系;特别是在以化学耦合为主的混合突触网络里,仅当兴奋性突触与抑制性突触比例约为4:1时,噪声才可诱导网络产生共振行为.在此比例下,引入部分时滞发现时滞可诱导网络产生随机多共振,且随网络中时滞边比例的增加,系统响应强度达到最优水平的时滞取值区间逐渐变窄;同时发现,网络中含有的化学突触越多,部分时滞诱导产生的多共振行为越强.此外,当时滞为系统固有周期的整数倍时,时滞越大共振所对应的噪声区域越广;并且网络中时滞边越多,越容易促使噪声和时滞诱导其产生明显的共振行为.     

Doubly stochastic coherence via noise-induced symmetry in bistable neural models

The generation of coherent dynamics due to noise in an activator-inhibitor system describing bistable neural dynamics is investigated. We show that coherence can be induced in deterministically asymmetric regimes via symmetry restoration by multiplicative noise, together with the action of additive noise which induces jumps between the two stable steady states. The phenomenon is thus doubly stochastic, because both noise sources are necessary. This effect can be understood analytically in the frame of a small-noise expansion and is confirmed experimentally in a nonlinear electronic circuit. Finally, we show that spatial coupling enhances this coherent behavior in a form of system-size coherence resonance.     

Doubly stochastic resonance

We report the effect of doubly stochastic resonance which appears in nonlinear extended systems if the influence of noise is twofold: A multiplicative noise induces bimodality of the mean field of the coupled network and an independent additive noise governs the dynamic behavior in response to small periodic driving. For optimally selected values of the additive noise intensity stochastic resonance is observed, which is manifested by a maximal coherence between the dynamics of the mean field and the periodic input. Numerical simulations of the signal-to-noise ratio and theoretical results from an effective two state model are in good quantitative agreement.     

Coherence Resonance and Noise-Induced Synchronization in Hindmarsh-Rose Neural Network with Different Topologies

In this paper, we investigate coherence resonance （CR） and noise-induced synchronization in Hindmarsh- Rose （HR） neural network with three different types of topologies： regular, random, and small-world. It is found that the additive noise can induce CR in HR neural network with different topologies and its coherence is optimized by a proper noise level. It is also found that as coupling strength increases the plateau in the measure of coherence curve becomes broadened and the effects of network topology is more pronounced simultaneously. Moreover, we find that increasing the probability p of the network topology leads to an enhancement of noise-induced synchronization in HR neurons network.     

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.     

Coloured noise influence on system evolution

Within the power-law approach for noise amplitude dependence on stochastic variables, we present a picture of noise-induced transitions in systems affected by coloured multiplicative noise. The governed equations for main statistical moments are obtained and investigated in detail. We show that a reentrant noise-induced transition is realized within a window of the control parameter. Received 15 October 2001 / Received in final form 8 July 2002 Published online 17 September 2002     

Noise-induced phase synchronization and synchronization transitions in chaotic oscillators

Whether common noise can induce complete synchronization in chaotic systems has been a topic of great relevance and long-standing controversy. We first clarify the mechanism of this phenomenon and show that the existence of a significant contraction region, where nearby trajectories converge, plays a decisive role. Second, we demonstrate that, more generally, common noise can induce phase synchronization in nonidentical chaotic systems. Such a noise-induced synchronization and synchronization transitions are of special significance for understanding neuron encoding in neurobiology.     

Coherence resonance and stochastic synchronization in a nonlinear circuit near a subcritical Hopf bifurcation

We analyze noise-induced phenomena in nonlinear dynamical systems near a subcritical Hopf bifurcation. We investigate qualitative changes of probability distributions (stochastic bifurcations), coherence resonance, and stochastic synchronization. These effects are studied in dynamical systems for which a subcritical Hopf bifurcation occurs. We perform analytical calculations, numerical simulations and experiments on an electronic circuit. For the generalized Van der Pol model we uncover the similarities between the behavior of a self-sustained oscillator characterized by a subcritical Hopf bifurcation and an excitable system. The analogy is manifested through coherence resonance and stochastic synchronization. In particular, we show both experimentally and numerically that stochastic oscillations that appear due to noise in a system with hard excitation, can be partially synchronized even outside the oscillatory regime of the deterministic system.     

Control of stochastic resonance in bistable system by using periodic signal

<正>According to the characteristic structure of double wells in bistable systems,this paper analyses stochastic fluctuations in the single potential well and probability transitions between the two potential wells and proposes a method of controlling stochastic resonance by using a periodic signal.Results of theoretical analysis and numerical simulation show that the phenomenon of stochastic resonance happens when the time scales of the periodic signal and the noise-induced probability transitions between the two potential wells achieve stochastic synchronization.By adding a bistable system with a controllable periodic signal,fluctuations in the single potential well can be effectively controlled,thus affecting the probability transitions between the two potential wells.In this way,an effective control can be achieved which allows one to either enhance or realize stochastic resonance.     

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.     

Infection dynamics in structured populations with disease awareness based on neighborhood contact history

It is well-known that the climate system, due to its nonlinearity, can be sensitive to stochastic forcing. New types of dynamical regimes caused by the noise-induced transitions are revealed on the basis of the classical climate model previously developed by Saltzman with co-authors and Nicolis. A complete parametric classification of dynamical regimes of this deterministic model is carried out. On the basis of this analysis, the influence of additive and parametric noises is studied. For weak noise, the climate system is localized nearby deterministic attractors. A mixture of the small and large amplitude oscillations caused by noise-induced transitions between equilibria and cycle attraction basins arise with increasing the noise intensity. The portion of large amplitude oscillations is estimated too. The parametric noise introduced in two system parameters demonstrates quite different system dynamics. Namely, the noise introduced in one system parameter increases its dispersion whereas in the other one leads to the stabilization of the climatic system near its unstable equilibrium with transitions from order to chaos.     

Delay-aided stochastic multiresonances on scale-free FitzHugh-Nagumo neuronal networks

The stochastic resonance in paced time-delayed scale-free FitzHugh-Nagumo(FHN) neuronal networks is investigated.We show that an intermediate intensity of additive noise is able to optimally assist the pacemaker in imposing its rhythm on the whole ensemble.Furthermore,we reveal that appropriately tuned delays can induce stochastic multiresonances,appearing at every integer multiple of the pacemaker’s oscillation period.We conclude that fine-tuned delay lengths and locally acting pacemakers are vital for ensuring optimal conditions for stochastic resonance on complex neuronal networks.     

Stochastic resonance and noise delayed extinction in a model of two competing species

We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka–Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence of a periodic driving term, which accounts for the environment temperature variation. We find noise-induced periodic oscillations of the species concentrations and stochastic resonance phenomenon. We find also a nonmonotonic behavior of the mean extinction time of one of the two competing species as a function of the additive noise intensity.     

Stochastic resonance on a modular neuronal network of small-world subnetworks with a subthreshold pacemaker

We study the phenomenon of stochastic resonance on a modular neuronal network consisting of several small-world subnetworks with a subthreshold periodic pacemaker. Numerical results show that the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the intensity of additive spatiotemporal noise. This effect of pacemaker-driven stochastic resonance of the system depends extensively on the local and the global network structure, such as the intra- and inter-coupling strengths, rewiring probability of individual small-world subnetwork, the number of links between different subnetworks, and the number of subnetworks. All these parameters play a key role in determining the ability of the network to enhance the noise-induced outreach of the localized subthreshold pacemaker, and only they bounded to a rather sharp interval of values warrant the emergence of the pronounced stochastic resonance phenomenon. Considering the rather important role of pacemakers in real-life, the presented results could have important implications for many biological processes that rely on an effective pacemaker for their proper functioning.     

Influence of Coupling Delay on Noise Induced Coherent Oscillations in Excitable Systems

Influence of small time-delays in coupling between noisy excitable systems on the coherence resonance and self-induced stochastic resonance is studied. Parameters of delayed coupled deterministic excitable units are chosen such that the system has only one attractor, namely the stationary state, for any value of the coupling and the time-lag. Addition of white noise induces qualitatively different types of coherent oscillations, and we analyzed the influence of coupling time-delay on the properties of these coherent oscillations. The main conclusion is that time-lag τ≥1, but still smaller than the refractory period, and sufficiently strong coupling drastically change signal to noise ratio in the quantitative and qualitative way. An interval of noise values implies quite large signal to noise ratio and different types of noise induced coherence are greatly enhanced. We also observed coincident spiking for small noise intensity and time-lag proportional to the inter-spike interval of the coherent spike trains. On the other hand, time-lags τ<1 and/or weak coupling induce negligible changes in the properties of the stochastic coherence.     

乘性噪音和加性噪音效应对脉孢菌生物钟体系内信号随机共振的增强

利用有和无外信号作用的脉孢菌生物钟体系,研究了与加性噪音相关或不相关的乘性噪音对加性噪音诱导出的内信号随机共振的影响作用.结果表明：无外信号的情况下,不论加性和乘性噪音相关与否,当乘性噪音强度小于临界值时,乘性噪音的加入使加性噪音诱导产生的内随机共振强度得到增强;当大于其临界值时,加性噪音的随机共振强度却得不到进一步增强,这说明脉孢菌生物钟体系能抵抗外噪音的干扰而维持自身的生理节奏.当加入外信号时,对于乘性和加性噪音不相关的情况,发现存在最佳频率（0.003 Hz）的外信号能使加性噪音诱导出的内信号随机共 关键词： 噪音 脉孢菌生物钟体系 内信号随机共振     

Stochastic dynamics of the cubic map: A study of noise-induced transition phenomena

The effects of finite-amplitude, additive noise on the dynamics generated by a one-dimensional, two-parameter cubic map are considered. The underlying deterministic system exhibits bistability and hysteresis, and noise-induced processes associated with these phenomena are studied. If a bounded noise source is applied to this system, trajectories may be confined to a finite region. Mechanisms are given for the merging transitions between different parts of this region and the eventual escape from it as the noise level is increased. The noisy dynamics is also represented by an integral evolution operator, with an equilibrium density function with finite support. The operator's spectrum is determined as a function of map parameters and noise amplitude. Such noisy one-dimensional maps can provide models for the study of noise-induced phenomena described by stochastic differential equations.     

Noise-induced Hopf-bifurcation-type sequence and transition to chaos in the lorenz equations

We study the effects of noise on the Lorenz equations in the parameter regime admitting two stable fixed point solutions and a strange attractor. We show that noise annihilates the two stable fixed point attractors and evicts a Hopf-bifurcation-like sequence and transition to chaos. The noise-induced oscillatory motions have very well defined period and amplitude, and this phenomenon is similar to stochastic resonance, but without a weak periodic forcing. When the noise level exceeds certain threshold value but is not too strong, the noise-induced signals enable an objective computation of the largest positive Lyapunov exponent, which characterize the signals to be truly chaotic.     

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.     

Self-induced stochastic resonance in excitable systems

The effect of small-amplitude noise on excitable systems with strong time-scale separation is analyzed. It is found that vanishingly small random perturbations of the fast excitatory variable may result in the onset of a deterministic limit cycle behavior, absent without noise. The mechanism, termed self-induced stochastic resonance, combines a stochastic resonance-type phenomenon with an intrinsic mechanism of reset, and no periodic drive of the system is required. Self-induced stochastic resonance is different from other types of noise-induced coherent behaviors in that it arises away from bifurcation thresholds, in a parameter regime where the zero-noise (deterministic) dynamics does not display a limit cycle nor even its precursor. The period of the limit cycle created by the noise has a non-trivial dependence on the noise amplitude and the time-scale ratio between fast excitatory variables and slow recovery variables. It is argued that self-induced stochastic resonance may offer one possible scenario of how noise can robustly control the function of biological systems.