双层Hodgkin-Huxley神经元网络中的随机共振

随机共振是一种非零噪声优化系统响应的现象。运用信噪比的评价方式,研究单个Hodgkin-Huxley神经元及其所构建的双层神经元网络中的随机共振,来模拟生物感觉系统中检测微弱信号的随机共振现象。结果表明,单个神经元在阈值下存在噪声优化系统检测性能的随机共振现象,但是最优的噪声强度却随外部信号性质的改变而变化;双层神经元网络不但可以在固定的噪声强度上对一定幅度范围内的阈下信号进行优化检测,而且噪声的存在并没有降低网络对阈上信号的检测能力。     

一类随机环境中恒化器模型的动力学行为分析

考虑到环境中噪声的影响建立了一类随机恒化器模型.首先,利用比较定理验证了模型正解的全局存在唯一性;其次,证明了当噪声强度较小时随机模型的解将围绕相应确定性模型的平衡点振荡,而强度较大的噪声可引起微生物的整体溢出;另外,根据Hasminskii定理说明了模型平稳分布的存在性;最后,通过数值模拟验证了所得理论结果的正确性.     

污染环境中具有Markov切换的随机三种群竞争系统生存分析

本文研究污染环境下受到毒素和双重噪声(白噪声和有色噪声)作用的随机系统,建立污染环境中具有Markov切换的随机三种群竞争模型.一方面,本文得到系统中各种群灭绝、随机非平均持久的充分条件;另一方面,考虑到系统中竞争作用对种群生存状态产生的影响,本文得到系统中各种群随机弱平均持久及随机强平均持久的充分条件.文末也通过数值模拟显示出相应的理论结果.     

逆重复伪随机序列信号相关分析法在探测蝇复眼电反应中的应用

伪白噪声测试信号的相关分析法,对于黑箱辨识问题来说,是较为合适的实验手段。隨着这种方法应用的扩展,特别是应用于生理系统,提出了如何进一步选择合适的输入信号的问题。逆重复伪随机二进制序列是较为合适的。本文介绍了逆重复伪随机序列信号相关分析法在探测光引起的蝇复眼反应中的应用,描述了信号的产生,测量并计算了模拟输出,它和实测结果甚为符合,说明这种方法对预测反应具有较高的精确性     

随机力对激光育种频率影响的研究

本文对ＤＮＡ分子势场用辏力场近似,建立了该近似了Ｆｏｋｋｅｒ－Ｐｌａｎｃｋ方程并用数值法求解了本征值,发现处于生物体内的ＤＮＡ分子,由于受随机力噪声作用,影响了能级分立状态,使其振吸收频率拓宽,从而使激光育种中使用有效激光范围较广。     

一类随机时滞捕食者-食饵模型的动力学行为（英文）

研究了一类含时滞的Harrison型捕食者-食饵模型在随机扰动环境下的动力学行为.对于非时滞和时滞模型分别给出了局部和全局稳定性条件.通过白噪声分别对食饵人口增长率的和捕食者人口死亡率进行随机扰动,构建相应的随机时滞微分方程模型讨论环境噪声对其作用的动力学行为.在一定条件下,随机时滞模型存在随机最终有界的唯一全局正解且解的二阶均值是有界的.最后通过数值模拟对给出的分析结果进行了验证.     

随机进化稳定性研究进展

在过去的三十多年, 演化博弈理论及其进化稳定对策的概念不仅被广泛地应用于解释动物行为的进化, 而且也被成功地应用于分子生物学、经济学、政治学和社会学等诸多学科。然而, 在随机波动环境中演化博弈动态的随机动力学性质始终没有被清晰地认识, 并且这是一个极具挑战性的理论问题。本文简单介绍了我们最近所提出的随机进化稳定性(stochastic evolutionary stability, SES)的概念。随机进化稳定性不仅是经典进化稳定对策(evolutionarily stably strategy, ESS)概念在随机环境下的自然扩展, 而且为揭示在随机环境中动物行为的演化动态提供一个基本的理论框架。     

感觉神经放电中的随机共振现象和噪声的作用

随机共振现象是非线性系统中普遍存在的自然现象 ,其中 ,噪声可以帮助检测弱信号而不是淹没弱信号。本文介绍了感觉神经放电活动中的随机共振现象和产生的机制 ,揭示了神经系统利用噪声检测弱信号的机制 ,并提出了随机共振在神经系统信息处理中的可能作用。     

一类随机SIR流行病模型的渐近行为研究

考虑了一类恢复率受到噪声影响的随机SIR流行病模型.首先证明了模型非负解的全局存在惟一性;其次证明了当基本再生数R₀≤1时无病平衡点随机渐近稳定,当R₀>1时随机模型的解围绕确定性模型地方病平衡点震荡.最后通过数值仿真验证了所得结论的正确性.     

噪声诱导多细胞系统的同步切换

在以往的工作中讨论了对单细胞的基因开关系统噪声如何诱导连贯切换．在此,对多细胞的基因开关网络系统研究各种噪声（包括细胞内噪声和细胞环境噪声）对同步切换的影响．发现：细胞内基因调控过程中的合成率和降解率的随机涨落以及细胞内的附加噪声均能够诱导群体基因开关系统的同步切换,而且存在一个最优的噪声强度,它使得这种同步切换的效果最佳．另一方面,细胞环境的随机涨落所导致的噪声（即环境噪声）,不但能诱导上述同步切换,而且当细胞内噪声不足以诱导细胞群体的同步切换时,它通过压制内部噪声来达到增强群体系统的协作行为．最后,还分析了受噪声影响的信号分子的扩散率对细胞群体切换行为的影响．     

Harvesting in a random environment: Itô or Stratonovich calculus?

We extend to harvesting stochastic differential equation (SDE) models in a random environment our previous work on models without harvesting concerning the resolution of the It?-Stratonovich controversy. The resolution is obtained for the very general class of models dN/dt=N (r(N)-h(N)+sigmaepsilon(t)), where N=N(t) is the population size at time t, r(N) is the (density-dependent) "mean" per capita growth rate, h(N) is the (density-dependent) harvesting effort, epsilon(t) is a standard white noise (representing environmental random fluctuations), and sigma is a noise intensity parameter. It? and Stratonovich calculus in the resolution of SDEs apparently give different qualitative and quantitative results, leading to controversy on which calculus is more appropriate and creating an obstacle on the use of this modeling approach. We show that the apparent difference between the two calculi is due to a semantic confusion based on the fallacious assumption that we are working with the same type of mean rates. After clearing the confusion, the two calculi yield exactly the same results and we obtain important common conditions for extinction and for existence of a stationary density. The resolution of the controversy is intertwined with and sheds light on the estimation issues.     

Seidel–Herzel model of human baroreflex in cardiorespiratory system with stochastic delays

The stochastic versus deterministic solution of the Seidel–Herzel model describing the baroreceptor control loop (which regulates the short-time heart rate) are compared with the aim of exploring the heart rate variability. The deterministic model solutions are known to bifurcate from the stable to sustained oscillatory solutions if time delays in transfer of signals by sympathetic nervous system to the heart and vasculature are changed. Oscillations in the heart rate and blood pressure are physiologically crucial since they are recognized as Mayer waves. We test the role of delays of the sympathetic stimulation in reconstruction of the known features of the heart rate. It appears that realistic histograms and return plots are attainable if sympathetic time delays are stochastically perturbed, namely, we consider a perturbation by a white noise. Moreover, in the case of stochastic model the bifurcation points vanish and Mayer oscillations in heart period and blood pressure are observed for whole considered space of sympathetic time delays.      

Stochastic models for inferring genetic regulation from microarray gene expression data

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information.     

Optimal harvesting of stochastically fluctuating populations

 We obtain the optimal harvesting plan to maximize the expected discounted number of individuals harvested over an infinite future horizon, under the most common (Verhulst-Pearl) logistic model for a stochastically fluctuating population. We also solve the problem for the standard variants of the model where there are constraints on the admissible harvesting rates. We use stochastic calculus to derive the optimal population threshold at which individuals are harvested as well as the overall value of the population in the sense of the model. We show that except under extreme conditions, the population is never depleted in finite time, but remains in a stationary distribution which we find explicitly. Needless to say, our results prove that any strategy which totally depletes the population is sub-optimal. These results are much more precise than those previously obtained for this problem. Received 24 June 1996; received in revised form 7 April 1997     

Bayesian inference for stochastic kinetic models using a diffusion approximation

This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behavior and the model is identified using equispaced time course data. The estimation framework involves the introduction of m- 1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic autoregulatory gene network.     

Weak-Periodic Stochastic Resonance in a Parallel Array of Static Nonlinearities

This paper studies the output-input signal-to-noise ratio (SNR) gain of an uncoupled parallel array of static, yet arbitrary, nonlinear elements for transmitting a weak periodic signal in additive white noise. In the small-signal limit, an explicit expression for the SNR gain is derived. It serves to prove that the SNR gain is always a monotonically increasing function of the array size for any given nonlinearity and noisy environment. It also determines the SNR gain maximized by the locally optimal nonlinearity as the upper bound of the SNR gain achieved by an array of static nonlinear elements. With locally optimal nonlinearity, it is demonstrated that stochastic resonance cannot occur, i.e. adding internal noise into the array never improves the SNR gain. However, in an array of suboptimal but easily implemented threshold nonlinearities, we show the feasibility of situations where stochastic resonance occurs, and also the possibility of the SNR gain exceeding unity for a wide range of input noise distributions.     

Stochastic analogues of deterministic single-species population models

Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models--additive normally distributed noise and multiplicative lognormally distributed noise--generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.     

Statistical interpretation of the interplay between noise and chaos in the stochastic logistic map

A recurring problem in population biology - as well as other stochastic dynamical systems in biology, the physical and social sciences - is the distinction between the ‘true’ dynamics of a system and observational noise: i.e. can we from present data reliably infer e.g. biological mechanisms, or are signals swamped by noise.Here, we approach this problem using the canonical model for simple systems that exhibit complex behaviour, the logistic map. At each time-point noise is added, which allows us to study the long-term behaviour of a system which exhibits both non-linear dynamics and intrinsic noise.We show that the interplay between deterministic non-linear dynamics and simple Gaussian noise results in a perplexingly simple system when viewed statistically.In particular we show that for the case of Gaussian noise it is possible to derive at very reliable approximations for the time until the system has reached an absorbing state. This generic model allows us, for example, to study the life-time of molecular species involved in noisy feedback loops.     

Stochastic functional data analysis: a diffusion model-based approach

This article presents a new modeling strategy in functional data analysis. We consider the problem of estimating an unknown smooth function given functional data with noise. The unknown function is treated as the realization of a stochastic process, which is incorporated into a diffusion model. The method of smoothing spline estimation is connected to a special case of this approach. The resulting models offer great flexibility to capture the dynamic features of functional data, and allow straightforward and meaningful interpretation. The likelihood of the models is derived with Euler approximation and data augmentation. A unified Bayesian inference method is carried out via a Markov chain Monte Carlo algorithm including a simulation smoother. The proposed models and methods are illustrated on some prostate-specific antigen data, where we also show how the models can be used for forecasting.     

Finding optimal vaccination strategies under parameter uncertainty using stochastic programming

We present a stochastic programming framework for finding the optimal vaccination policy for controlling infectious disease epidemics under parameter uncertainty. Stochastic programming is a popular framework for including the effects of parameter uncertainty in a mathematical optimization model. The problem is initially formulated to find the minimum cost vaccination policy under a chance-constraint. The chance-constraint requires that the probability that R(*) 相似文献