生物钟基因网络中分子噪声诱导的日夜节律振荡及相干共振

研究了果蝇细胞内生物钟基因调节网络的分子噪声，特别讨论了生物钟系统处于略微远离振荡区域的稳态时分子噪声对于时钟蛋白的日夜节律振荡的影响.结果表明：(1)虽然时钟蛋白合成或者衰减的生化反应事件是在随机的时间间隔里随机发生的，但系统可以依赖自身固有的调节机理诱导出明显的日夜节律振荡；(2)分子噪声诱导的日夜节律振荡的相干性可以在合适的分子噪声水平下到达最佳，说明了相干共振现象的发生.     

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 .     

生物钟基因网络中分子噪声诱导的日夜节律振荡及相干共振

研究了果蝇细胞内生物钟基因调节网络的分子噪声，特别讨论了生物钟系统处于略微远离振荡区域的稳态时分子噪声对于时钟蛋白的日夜节律振荡的影响.结果表明：(1)虽然时钟蛋白合成或者衰减的生化反应事件是在随机的时间间隔里随机发生的，但系统可以依赖自身固有的调节机理诱导出明显的日夜节律振荡；(2)分子噪声诱导的日夜节律振荡的相干性可以在合适的分子噪声水平下到达最佳，说明了相干共振现象的发生. 关键词： 生物钟 分子噪声 日夜节律振荡 相干共振     

模型化研究两细胞间基因、蛋白耦合振荡中的噪声效应

本文基于Hill动力学与Michaelis-Menten方程，建立理论模型研究两细胞间基因、蛋白耦合振荡中的噪声效应.研究发现，在Notch信号通路中，两细胞间基因、蛋白耦合振荡呈现了周期振荡特性，表明了细胞间信号传导的同步振荡特性.“内在”噪声和“外在”噪声对两细胞间基因、蛋白耦合振荡有着不同的作用.内噪声有利于细胞间Notch信号通路中各基因、蛋白表达再次提升.外噪声诱导通路中基因、蛋白的表达水平降低，周期振荡变得阻尼.内、外噪声共同作用不仅可使得基因表达适当并呈现出持续振荡模式，而且还可使得细胞间基因转录合成相应的蛋白过程呈现出持续振荡模式.从而表明了基因表达的内、外噪声共同作用有利于控制细胞间基因激活、蛋白合成保持周期节律性.本文理论结果揭示了内外噪声对细胞间Notch信号通路动力学的一种调控机制，确定了内外噪声各自的调控效应，澄清了内外噪声共同作用调控体系持续周期振荡的物理机制，理论结果符合实验，可为设计阻止Notch体系基因、蛋白变异导致的多种疾病和癌症的通路治疗方案提供理论依据.     

Coherent Resonance for Rate Oscillations During CO Oxidation on Pt(110) Surfaces: Interplay Between Internal and External Noise

用理论和模拟相结合的方法研究了Pt(110)面上CO催化氧化体系中由化学反应随机性所导致的内涨落和参量扰动带来的外涨落对其速率振荡过程的影响,重点考察了内涨落和外涨落的相互作用．在体系的确定性Hopf分岔点附近区域,噪声可以诱导产生随机振荡,其信噪比随噪声强度的变化会出现极大值,即发生了相干共振．运用随机范式理论,研究发现体系的相干共振行为依赖于一\有效噪声",其强度是内涨落和外涨落的加权和．研究结果表明,在内外噪声强度的参数平面内,随机振荡的信噪比呈现屋脊形,太大的内涨落或外涨落条件下相干共振都不能发生．数值模拟的结果和理论分析符合得很好．     

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     

System Size Resonance Associated with Canard Phenomenon in a Biological Cell System

通过研究发现，内噪声对细胞内钙振荡是有影响的，当体系处于由确定性方程所确定的稳定区域时，如果考虑内噪声的作用，就会有随机的钙振荡发生. 并且这种振荡的行为随着体系尺度的变化出现两个最大值，表明了尺度共振现象的发生. 这种行为是与体系的Canard现象密切相关的. 最佳的体系尺度与真实的细胞体积是相吻合的，并且这种吻合基本不随控制参数的改变而改变.     

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     

噪声交叉关联强度的时间周期调制对线性过阻尼系统的随机共振的影响

针对由加性、乘性噪声和周期信号共同作用的线性过阻尼系统, 在噪声交叉关联强度受到时间周期调制的情况下,利用随机平均法推导了系统响应的信噪比的解析表达式. 研究发现这类系统比噪声间互不相关或噪声交叉关联强度为常数的线性系统具有更丰富的动力学特性, 系统响应的信噪比随交叉关联调制频率的变化出现周期振荡型随机共振, 噪声的交叉关联参数导致随机共振现象的多样化.噪声交叉关联强度的时间周期调制的引入有利于提高对微弱周期信号检测的灵敏度和实现对周期信号的频率估计. 关键词： 随机共振 周期振荡型共振 噪声交叉关联强度 信噪比     

二维映射神经元模型中的相干双共振

在具有稳定次阈值振荡特性的二维映射神经元模型中,研究了在没有外界输入信号时噪声对体系动力学的影响.通过数值计算发现了当体系的确定性动力学处于静息状态时,噪声可以诱导出神经元膜电位的随机振荡,而且随着噪声强度的变化,这种振荡的相干性具有两个极大值.另外我们还研究了当体系的确定性动力学处于稳定次阈值振荡及神经脉冲状态时的噪声效应,结果表明噪声对体系动力学的影响与其确定性动力学的分岔特性密切相关.     

Noise-induced chaos in non-linear dynamics of El Niños

Motivated by an important practical significance, we analyze the noise-induced El Niño evolutionary equations. Our analysis based on the evaluation of largest Lyapunov exponents demonstrates the new effects of deterministic and stochastic dynamics of the El Niño–Southern Oscillation Events. We show that the non-linear deterministic model possesses either a multiturn limit cycle with regular self-oscillations or chaotic oscillations depending on slight variations of one of the main system parameters – the mean tropical easterlies. It is revealed that in the presence of noise, transformations of regular oscillations into chaotic ones are observed.     

Intrinsic noise and division cycle effects on an abstract biological oscillator

Oscillatory dynamics are common in biological pathways, emerging from the coupling of positive and negative feedback loops. Due to the small numbers of molecules typically contained in cellular volumes, stochastic effects may play an important role in system behavior. Thus, for moderate noise strengths, stochasticity has been shown to enhance signal-to-noise ratios or even induce oscillations in a class of phenomena referred to as "stochastic resonance" and "coherence resonance," respectively. Furthermore, the biological oscillators are subject to influences from the division cycle of the cell. In this paper we consider a biologically relevant oscillator and investigate the effect of intrinsic noise as well as division cycle which encompasses the processes of growth, DNA duplication, and cell division. We first construct a minimal reaction network which can oscillate in the presence of large or negligible timescale separation. We then derive corresponding deterministic and stochastic models and compare their dynamical behaviors with respect to (i) the extent of the parameter space where each model can exhibit oscillatory behavior and (ii) the oscillation characteristics, namely, the amplitude and the period. We further incorporate division cycle effects on both models and investigate the effect of growth rate on system behavior. Our results show that in the presence but not in the absence of large timescale separation, coherence resonance effects result in extending the oscillatory region and lowering the period for the stochastic model. When the division cycle is taken into account, the oscillatory region of the deterministic model is shown to extend or shrink for moderate or high growth rates, respectively. Further, under the influence of the division cycle, the stochastic model can oscillate for parameter sets for which the deterministic model does not. The division cycle is also found to be able to resonate with the oscillator, thereby enhancing oscillation robustness. The results of this study can give valuable insight into the complex interplay between oscillatory intracellular dynamics and various noise sources, stemming from gene expression, cell growth, and division.     

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.     

Bounding the quality of stochastic oscillations in population models

We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. Although usually defined a priori, the deterministic version of these models can be obtained as the infinite volume limit of many stochastic models (which are necessarily defined by more parameters than the deterministic one). It is known that damped oscillations in a deterministic model usually correspond to oscillatory-like fluctuations in their deterministic counterparts. The quality of these “oscillations" depends on details of each stochastic model. We show, however, that the parameters of the deterministic system are generally enough to obtain very good bounds for the quality of “oscillations" in any of its stochastic counterparts. These bounds are shown to depend on only one dimensionless parameter.     

Analysis of noise-induced eruptions in a geyser model

Motivated by important geophysical applications we study a non-linear model of geyserdynamics under the influence of external stochastic forcing. It is shown that thedeterministic dynamics is substantially dependent on system parameters leading to thefollowing evolutionary scenaria: (i) oscillations near a stable equilibrium and atransient tendency of the phase trajectories to a spiral sink or a stable node(pre-eruption regime), and (ii) fast escape from equilibrium (eruption regime). Even asmall noise changes the system dynamics drastically. Namely, a low-intensity noisegenerates the small amplitude stochastic oscillations in the regions adjoining to thestable equilibrium point. A small buildup of noise intensity throws the system over itsseparatrix and leads to eruption. The role of the friction coefficient and relativepressure in the deterministic and stochastic dynamics is studied by direct numericalsimulations and stochastic sensitivity functions technique.     

Stochastic sensitivity analysis of noise-induced intermittency and transition to chaos in one-dimensional discrete-time systems

We study a phenomenon of noise-induced intermittency for the stochastically forced one-dimensional discrete-time system near tangent bifurcation. In a subcritical zone, where the deterministic system has a single stable equilibrium, even small noises generate large-amplitude chaotic oscillations and intermittency. We show that this phenomenon can be explained by a high stochastic sensitivity of this equilibrium. For the analysis of this system, we suggest a constructive method based on stochastic sensitivity functions and confidence intervals technique. An explicit formula for the value of the noise intensity threshold corresponding to the onset of noise-induced intermittency is found. On the basis of our approach, a parametrical diagram of different stochastic regimes of intermittency and asymptotics are given.