嗅觉系统神经网络模型的模拟与动力学特性分析

在哺乳动物嗅觉系统的拓扑结构及生理实验的基础上建立了一套非线性动力学神经网络模型．此模型在模拟嗅觉神经系统方面有着突出的优点,同时在信号处理以及模式识别中表现出了奇异的混沌特性．着重描述了K系列模型的非线性动力学特性,并通过数值模拟进行分析．     

表达新城疫病毒F48E8株血凝素—神经氨酸酶的重组鸡痘病毒的构建 …

在克隆和鉴定新城疫病毒（ＮＤＶ）Ｆ４８Ｅ８株血凝素－神经氨酸酶（ＨＮ）基因的基础上,应用分子克隆技术将ＨＮ基因导入鸡痘病毒插入载体ｐＦＧ１１７５－１中启动子Ｐ７．５的下游,得到携带ＮＤＶ－ＨＮ基因的质粒ｐＦＧＨＮ１１７５－１。将此质粒ｐＦＧＨＮ１１７５－１以脂质体转染中国鸡痘病毒疫苗株２８２Ｅ４株感染３￣４ｈ的鸡胚成纤维细胞,采用蓝斑筛选方法纯化３次,得到稳定的重组鸡痘病毒。用ＮＤＶ－ＨＮ基因特异     

神经电路广义模糊逻辑骨架及其在视皮层神经系统模拟中的应用

大规模神经系统的非线性动力学特性分析是一件十分困难的工作. 本研究试图通过对神经细胞的动力学方程的研究, 探讨神经细胞的模糊逻辑骨架, 再由细胞的模糊逻辑骨架探讨神经系统的动力学特性与系统功能. 模糊逻辑与神经系统有密切的联系, 已有大量的文章报道这方面研究, 但是这类研究主要针对如何把模糊逻辑与神经网络的功能相结合产生具有一定控制或分类能力的系统. 与这些研究不同, 本研究是想把模糊逻辑作为研究非线性动力学的工具. 本文提出了模糊逻辑骨架的概念, 这样架构一个具有某种功能的神经系统就变得非常简便. 用这种方式构建了模拟初级视皮层功能的系统, 这个系统比一些已知的类似系统具有更多的功能.     

具有潜伏期的无免疫型传染病动力学模型的分析

研究了一类具有潜伏期的无免疫型传染病动力学模型,用摄动理论讨论分析了相应的非线性系统,得到了不同群体生存变化的渐近表达式,从而揭示了各种作用对不同群体生存影响的规律.本文的研究为解决一些类型的非线性模型提供了一种有效的方法.     

一类传染病动力学时滞模型的分析

研究了一类传染病动力学模型,用摄动理论讨论了相应的非线性时滞问题,得到了被传染病感染的人群数与健康人群数比例的变化规律的渐近表达式,从而揭示了传染病的潜伏期和传染期对疾病传播的影响和作用.本文的研究为解决这一类非线性时滞模型提供了一种有效的方法.     

非线性动力学在脑电信号分析中的应用

EEG是由大脑产生的非线性时间序列,体现出混沌行为。近年来迅速发展的非线性动力学理论为脑电信号分析开创了一个新的领域。本文综述了近年来非线性动力学在脑电信号研究中（睡眠阶段,麻醉深度,认知过程,精神分裂,痴呆及癫痫）的进展,以期对脑神经动力学有更好的理解。     

人心脏低维动力学模型的混沌控制

两个相互作用振子的非线性动力学行为由特定的一维双参量圆周映射概括。这一模型已经被成功地用于描述人心脏某些反常节律。本文将相加性开环加闭环（ＯＰＣＬ）控制机制引入人心脏低维动力学模型,设计了一种有效的、抗噪声干扰的控制技术,可以通过变更迫动项实现任意期望的周期轨道的稳定控制。计算机模拟实验证实：运用这种方法能够将相空间中任意的初始状态引导到预先规定的目标动力学状态。     

具非线性发病率随机SIQS传染病模型的渐近行为

研究了一类具有非线性发病率的随机SIQS传染病模型,通过构造适当的Lyapunov函数并结合遍历论的相关结论,探讨该模型的解在其平衡点附近的动力学行为.研究结果表明:当R_0≤1时,随机模型的解会沿着无病平衡点(A/d,0,0)附近振动;当R_01时,该模型在地方病平衡点附近存在遍历的不变分布.     

妊娠期抗癫痫药物的药代动力学变化及胎盘转运特征

癫痫是一种常见的神经系统慢性疾病,多数患者妊娠期需继续应用抗癫痫药物(AEDs)治疗,以控制癫痫发作。但妊娠期妇女体 内一系列生理变化可改变 AEDs 的药代动力学行为,导致癫痫发作并危及胎儿的生长发育。基于此,综述妊娠期 AEDs 的药代动力学变化 及胎盘转运特征,为妊娠期癫痫患者的精准合理用药提供参考。     

展望数学生态学与生态模型的未来

首先简要回顾了２０世纪数学生态学发展的历史,特别是半２个世纪以来在中国的发展。然后指出了生物学的进步为数学生态学的发展提供了机遇。作者列出了当前数学生态学和生态模型研究的几个热点：⑴非线性动力学;⑵种群的时空动态：包括异质种群动态,源－汇理论以及种群对时、空变化的响应等;⑶多样性和稳定性的关系;⑷行为的动态模型;⑸基于个体的模型。最后指出,生态学中混沌现象,可能表明多年来理论生态学家寻找的种群动态     

Stabilization of inhomogeneous patterns in a diffusion-reaction system under structural and parametric uncertainties

Many phenomena such as neuron firing in the brain, the travelling waves which produce the heartbeat, arrythmia and fibrillation in the heart, catalytic reactions or cellular organization activities, among others, can be described by a unifying paradigm based on a class of nonlinear reaction-diffusion mechanisms. The FitzHugh-Nagumo (FHN) model is a simplified version of such class which is known to capture most of the qualitative dynamic features found in the spatiotemporal signals. In this paper, we take advantage of the dissipative nature of diffusion-reaction systems and results in finite dimensional nonlinear control theory to develop a class of nonlinear feedback controllers which is able to ensure stabilization of moving fronts for the FHN system, despite structural or parametric uncertainty. In the context of heart or neuron activity, this class of control laws is expected to prevent cardiac or neurological disorders connected with spatiotemporal wave disruptions. In the same way, biochemical or cellular organization related with certain functional aspects of life could also be influenced or controlled by the same feedback logic. The stability and robustness properties of the controller will be proved theoretically and illustrated on simulation experiments.     

An analysis of a dendritic neuron model with an active membrane site

We formulate and analyze a mathematical model that couples an idealized dendrite to an active boundary site to investigate the nonlinear interaction between these passive and active membrane patches. The active site is represented mathematically as a nonlinear boundary condition to a passive cable equation in the form of a space-clamped FitzHugh-Nagumo (FHN) equation. We perform a bifurcation analysis for both steady and periodic perturbation at the active site. We first investigate the uncoupled space-clamped FHN equation alone and find that for periodic perturbation a transition from phase locked (periodic) to phase pulling (quasiperiodic) solutions exist. For the model coupling a passive cable with a FHN active site at the boundary, we show for steady perturbation that the interval for repetitive firing is a subset of the interval for the space-clamped case and shrinks to zero for strong coupling. The firing rate at the active site decreases as the coupling strength increases. For periodic perturbation we show that the transition from phase locked to phase pulling solutions is also dependent on the coupling strength.This work was supported in part by NSF Grants MCS 83-00562 and MDS 85-01535     

Integrate-and-fire models with nonlinear leakage

Can we express biophysical neuronal models as integrate-and-fire (IF) models with leakage coefficients which are no longer constant, as in the conventional leaky IF model, but functions of membrane potential and other biophysical variables? We illustrate the answer to this question using the FitzHugh-Nagumo (FHN) model as an example. A novel IF type model, the IF-FHN model, which approximates to the FHN model, is obtained. The leakage coefficient derived in the IF-FHN model has nonmonotonic relationship with membrane potential, revealing at least in part the intrinsic mechanisms underlying the FHN models. The IF-FHN model correspondingly exhibits more complex behaviour than the standard IF model. For example, in some parameter regions, the IF-FHN model has a coefficient of variation of the output interspike interval which is independent of the number of inhibitory inputs, being close to unity over the whole range, comparable to the FHN model as we noted previously (Brown et al., 1999).     

STOCHASTIC RESONANCE MEASURED BY THEMUTUAL INFORMATION IN THE NEURONSTHAT TRANSMIT CHAOTIC SPIKE TRAINS

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STOCHASTIC RESONANCE MEASURED BY THEMUTUAL INFORMATION IN THE NEURONSTHAT TRANSMIT CHAOTIC SPIKE TRAINS

The spike trains generated by a neuron model are studied by the methods of nonlinear time series analysis. The results show that the spike trains are chaotic. To investigate effect of noise on transmission of chaotic spike trains, this chaotic spike trains are used as a discrete subthreshold input signal to the integrate-and-fire neuronal model and the FitzHugh-Nagumo(FHN) neuronal model working in noisy environment. The mutual information between the input spike trains and the output spike trains is calculated, the result shows that the transformation of information encoded by the chaotic spike trains is optimized by some level of noise, and stochastic resonance(SR) measured by mutual information is a property available for neurons to transmit chaotic spike trains.     

A new method of identifying a systems based on the minimal quadratic discrepancy criterion for biophysics problems

A wide range of biophysical systems are described by nonlinear dynamic models mathematically presented as a set of ordinary differential equations in the Cauchy explicit form: [formula: see text] Fij(X1(t),..,XN(t),t), (i = 1,...,N, j = 1,...,M), where Fij (X1(t), ..., XN(t), t) is a set of basis functions satisfying the Lipschitz condition. We investigate the problem of evaluation of model constants aij (the system identification) using experimental data about the time dependence of the dynamic parameters of the system Xi(t). A new method of system identification for the class of similar nonlinear dynamic models is proposed. It is shown that the problem of identifying an initial nonlinear model can be reduced to the solution of a system of linear equations for the matrix of the dynamic model constants [aj]i. It is proposed to determine the set of dynamic model constants aij using the criterion of minimal quadratic discrepancy for the time dependence of the set of dynamic parameters Xi(t). An important special case of the nonlinear model, the quadratic model, is considered. Test problems of identification using this method are presented for two nonlinear systems: the Van der Pol type multiparametric nonlinear oscillator and the strange attractor of Ressler, a widely known example of dynamic systems showing the stochastic behavior.     

Reflecting the importance of human needs fulfilment in absolute sustainability assessments: Development of a sharing principle

Absolute environmental sustainability assessments (AESAs) evaluate whether the environmental impact of a product system is within its share of a safe operating space as determined by biophysical sustainability limits such as the planetary boundaries (PBs). The choice of sharing principle has significant influence on the result of an AESA, and any studies call for further research on how to share the safe operating space in an operational way that relates to the product's contribution to the welfare of the user. In this study, we develop the “Fulfilment of Human Needs” (FHN) principle as a sharing principle that operationalizes sufficientarianism (making sure everyone gets enough). The FHN principle is tested on two case studies (a food item and a textile) against four of the PBs: climate change, land-system change, water use, and nitrogen cycling. The operationalization of the FHN principle is slightly different between the PBs; the starting point for climate change is the average consumption pattern in countries classified as “most sustainable,” while for the other three PBs the status quo impact in the most sustainable countries is used. To operationalize the FHN principle on the product level, each consumption category is downscaled according to objective sources that determine the value delivered to the users. We demonstrate that, compared to other previously applied sharing principles, the FHN principle supports a stronger relation to the importance to the users of the delivered outcome.     

Computation of a Stabilizing Set of Feedback Matrices bf a Large-scale Nonlinear Musculoskeletal Dynamic Model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/ output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

Computation of a stabilizing set of feedback matrices of a large-scale nonlinear musculoskeletal dynamic model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

基于I/O特性的听觉非线性动态适应机制与前向掩蔽效应模型

听觉前向掩蔽效应是听觉动态非线性的重要表现, 也是听觉适应机制的重要表现, 由此产生听觉前后向参考编码机制,而传统的语音信号处理机制是帧与帧独立的线性处理方式,所以不能反映实际听觉系统的动态非线性适应特性。传统的听觉模型对这种动态非线性适应机制的模拟是通过自适应调节听觉耳蜗滤波器的增益来完成的, 这不管在计算量上还是在滤波器的稳定性设计上都有其缺陷。我们根据听觉的生理学机制,建立前馈自适应模型,从输入输出特性曲线上引出静态增益曲线,再在静态增益曲线上引入动态过程,由此建立的数学模型,利用心理学试验数据得到模型参数。试验结果表明,该模型能够很好地预测前向掩蔽效应,对听觉的动态非线性适应机制是一种很好的解释。