万有D'Alembert原理的统一形式

本文给出万有D'Alembert原理的统一形式,包含了现有的各种形式.     

四神经元时滞网络的稳定性与分岔

本文研究具有长连接的四神经元构成的时滞网络的稳定性与分叉.网络系统可采用一组含有多个时滞的非线性微分方程描述.通过分析网络零平衡点处线性近似系统特征方程的根的分布情况,给出了网络零平衡点全时滞局部渐近稳定条件和与时滞相关的局部渐近稳定条件.讨论网络平衡点的数目及稳定性,得到了网络静态分叉产生条件.以时滞为分叉参数,给出了零平衡点失稳后网络出现由Hopf分叉引起的周期运动的存在性条件.分叉周期运动的性质由网络的非线性因素确定.借助中心流形定理和规范型理论,得到了确定Hopf分叉方向,分叉周期运动稳定性和分叉周期运动周期的公式.最后给出数值算例,验证了理论分析的结果.研究表明:网络中长连接的强度和性质对网络的动力学行为有着重要的影响.     

相对论性万有D'Alembert原理的统一形式

本文给出相对论性万有 D'Alembert 原理的统一形式,它包括了现有相对论的各种形式,非相对论的各种形式只是本文的特例.     

基于神经网络与光纤传感阵列的结构状态监测方法

以探测机敏复合材料与结构内应变、应力及损伤等物理状态的位置信息为目的．提出了一种新颖的可内埋于材料与结构内作为结构状态监测用的强度调制型光纤传感阵列网络，并采用人工神经网络来处理传感阵列输出的并行分布式传感信号，阐述了适用的Ｋｏｈｏｎｅｎ网模型及其变化形式，给出了仿真实验结果     

一种等级有向道路网络模型及其生成算法

道路网络信息对GIS中的空间运算而言非常重要.基于单线有向道路基本网络模型,提出了一种等级有向道路网络模型用以支持大区域空间运算.在该模型中,现实世界道路网络被多个不同等级的有向网络描述,每个层次的道路网络信息都用单线单向道路网络表示.然后,在分析不同层次道路网络互操作信息需求的前提下,给出了基于低层次道路网络自动生成高层次网络的线性代价算法.最后,给出了自动生成等级有向道路网络的计算结果以及基于此模型的次最优快速最优路径算法计算结果.算法生成的道路网络可以较好支持大区域最优路径的计算,也可以对其他空间运算作很好的支持.     

大变位热弹性扁壳的一种边值模型

本文给出了正则形式基本方程及广义变分原理,并给出了关于应力函数、挠度、温度三种变量的一种边值模型。     

图论与复杂网络

近10年来迅猛发展起来的复杂网络理论为研究复杂性与复杂系统科学提供了一个重要支撑点,它高度概括了复杂系统的重要特征,无论是在理论还是在应用方面都具有很强的生命力,而且在各个方面都得到了很大发展.重点讨论图论在复杂网络中的应用,特别是代数图论在复杂网络同步问题中的应用.首先给出一些图的最小非零与最大特征值以及同步能力的估计,并且讨论了子图与图特征向量在同步能力估计中的作用.其次以两个简单图指出同步能力与网络结构参数的关系复杂,并给出补图与加边对同步研究的意义,然后给出图运算在复杂网络同步中的作用.最后从图论与控制理论角度展望了复杂网络领域未来可能的发展方向.      

两个新型的八结点块体单元—三维离散算子差分法

给出了弹性力学三维问题的离散算子差分法 ,讨论离散算子差分法在三维问题中的特点 ,意在为该方法的进一步发展提供依据 ,为应用弱形式进行数值求解的研究提供参考。本文从弹性力学平衡方程更为一般的弱形式出发 ,给出了含边界参数的弱形式方程。由该方程不仅可以得到有限元法 ,还可得到离散算子差分法。给出了两个八结点块体单元 ,虽然单元中位移函数是非协调的 ,不需特殊处理便可保证离散格式收敛 ,并对单元位移有十分好的反映能力。     

随机神经网络优化方法及其计算机仿真

研究了结构优化问题求解的随机神经网络方法,可较好地克服Hopfield网络方法容量陷入局部解的缺点,针对实例,对随机神经网络和Hopfield网络进行了动态仿真,直观地给出了两种网络的动态并行运行,能量函数的动态变化过程及两种网络的全局性的差异,同时也仿真出了网络并行运行至稳定优化解的时间。     

基于网络的数值分析系统

结合并行有限元分析以及Java分布式Web计算,介绍了基于网络的数值分析系统。首先介绍了系统的结构组成,进而给出系统的具体构建过程,并结合一些算例表明系统在土木工程中的实际应用,最后给出了结论。本系统将计算机网络技术以及面向对象的方法引入有限元分析以及土木工程领域,进行了有益的探索,研究可望将互联网变成工程师的日常工作中心。     

Stability criteria for periodic neural networks with discrete and distributed delays

In this paper, the stability analysis problem is dealt with for a class of periodic neural networks with both discrete and distributed time delays. Both global asymptotic and exponential stabilities are considered. The existence of the periodic solutions of the addressed neural networks is briefly discussed. Then, by constructing different Lyapnuov--Krasovskii functionals and using some analysis techniques, several new easy-to-test sufficient conditions are derived, respectively, for checking the globally asymptotic stability and globally exponential stability of the delayed neural networks. These results are useful in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for recurrent neural networks with mixed time delays. A simulation example is provided to demonstrate the effectiveness of the results obtained.     

STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES＊

The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions. By combining neural networks and wavelet theories, the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given. Based on wavelet networks, a new method for parameter identification was suggested, which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series. Through pre-treatment and comparison of results before and after the treatment, several useful conclusions are reached:High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.     

Exponential stability for switched Cohen–Grossberg neural networks with average dwell time

In this paper, uncertain switched Cohen–Grossberg neural networks with interval time-varying delay and distributed time-varying delay are proposed. Novel multiple Lyapunov functions are employed to investigate the stability of the switched neural networks under the switching rule with the average dwell time property. Sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) which guarantee the exponential stability for the switched Cohen–Grossberg neural networks. Numerical examples are provided to illustrate the effectiveness of the proposed method.     

Global Attractivity and Global Exponential Stability for Delayed Hopfield Neural Network Models

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Some methods of training radial basis neural networks in solving the Navier‐Stokes equations

The purpose of this research is to analyze the application of neural networks and specific features of training radial basis functions for solving 2‐dimensional Navier‐Stokes equations. The authors developed an algorithm for solving hydrodynamic equations with representation of their solution by the method of weighted residuals upon the general neural network approximation throughout the entire computational domain. The article deals with testing of the developed algorithm through solving the 2‐dimensional Navier‐Stokes equations. Artificial neural networks are widely used for solving problems of mathematical physics; however, their use for modeling of hydrodynamic problems is very limited. At the same time, the problem of hydrodynamic modeling can be solved through neural network modeling, and our study demonstrates an example of its solution. The choice of neural networks based on radial basis functions is due to the ease of implementation and organization of the training process, the accuracy of the approximations, and smoothness of solutions. Radial basis neural networks in the solution of differential equations in partial derivatives allow obtaining a sufficiently accurate solution with a relatively small size of the neural network model. The authors propose to consider the neural network as an approximation of the unknown solution of the equation. The Gaussian distribution is used as the activation function.     

Passivity analysis for discrete-time switched neural networks with various activation functions and mixed time delays

This paper is concerned with the passivity analysis for a class of discrete-time switched neural networks with various activation functions and mixed time delays. The mixed time delays under consideration include time-varying discrete delay and bounded distributed delay. By using the average dwell time approach and the discontinuous piecewise Lyapunov function technique, a novel delay-dependent sufficient condition for exponential stability of the switched neural networks with passivity is derived in terms of a set of linear matrix inequalities (LMIs). The obtained condition is not only dependent on the discrete delay bound, but also dependent on the distributed delay bound. A numerical example is given to demonstrate the effectiveness of the proposed result.     

用人工神经网络预测摩擦学系统磨损趋势

人工神经网络具有高度的并行分布式、联想记忆、自组织及自学习能力和极强的非线性映射能力，在许多领域显示了广阔的应用前景．但是，将神经网络用于摩擦学行为预测的研究报道却还鲜见．在对基于神经网络的单变量时间序列预测方法与过程进行分析之后，提出了摩擦学系统磨损趋势神经网络预测模型．采用定量铁谱参数中的总磨损Ｑ作为预测磨损趋势的特征参数，讨论了磨损趋势神经网络预测的单步预测法和多步预测法，并用其对ＣＤ４０齿轮泵的磨损趋势进行了预测，预测值与实测值吻合较好     

Prescribed-time adaptive neural tracking control for a class of uncertain robotic manipulators with dead zone input

This paper solves the prescribed-time control problem for a class of robotic manipulators with system uncertainty and dead zone input. To make the system stable within a given convergence time T, a novel prescribed-time adaptive neural tracking controller is proposed by using the temporal scale transformation method and Lyapunov stability theory. Unlike the finite-time and the fixed-time stability where the convergence time depends on the controller parameters, the convergence time constant T is introduced into the proposed controller so that the closed-loop system will be stable within T. To cope with the system uncertainty, radial basis function neural networks (RBFNNs) are used and only need to update one parameter online. In addition, by choosing the same structure and parameters of RBFNNs, the proposed method can shorten the convergence time of the neural networks. Finally, simulation results are presented to demonstrate the effectiveness of the prescribed-time controller.

     

The existence and exponential attractivity of κ-almost periodic sequence solution of discrete time neural networks

In the present paper, several sufficient conditions are obtained for the existence and exponential attractivity of a unique κ-almost periodic sequence solution of discrete time neural network. Our results generalize the corresponding results about almost periodic sequence solution in common sense. It is shown that discretization step κ affects the dynamical characteristics of discrete-time analogues of continuous time neural networks and exponential convergence is dependent on small discretization step size. Our results on exponential attractivity of κ-almost periodic sequence solution can provide us with relevant estimates on how precise such networks can perform during real-time computations. Finally, computer simulations are performed in the end to show the feasibility of our results.     

神经网络混沌运动的控制--CM方法

基于压缩映射的混沌控制方法——CM方法被应用到小的离散神经网络,通过一个外部输入的小干扰,稳定混沌轨道嵌入在混沌吸引子内的某一不稳周期轨上。利用闭回路对技术估计欲稳定周期轨的近似位置。给出二维和三维神经网络的典型例子,通过数值模拟显示CM方法控制离散神经网络混沌行为的简单和有效性。