胞映射技术研究非线性化学系统的性态

用胞映射方法对典型的非线性化学动力学系统,例如对著名的ＢＺ振荡反应、ＷＲ反应和Ｒｏｓｓｌｅｒ反应等复杂的非线性化学动力学体系的演化过程、内在机制、吸引环和振荡行为进行了数值仿真和分析,结果表明：胞映射方法能够揭示常规方法无法获取的内在规律和表象,进一步显示了胞映射方法普适性、定量性和求解性。     

胞映射基本理论与算法实现

胞映射方法是求解非线性复杂系统全局性态的一种数值计算技术,结合多线程并行处理的可视化技术,能够地对非线性化学动力学体系的复杂演化过程、奇异吸引域和混沌性态等进行有效、动态和准确地解析从而深刻揭示系统的内在机制。结合编程实践详细介绍ＨｓｕＣ．Ｓ创立的胞映射理论（包括简单胞映射和广义胞映射）的基本概念、算法实现框图、编程模块和应用技巧。讨论分析了胞映射方法的优势,结果表明：胞映射理论具有普遍适应性和求     

应用胞映射算法研究非线性化学模拟系统

用简单胞映射和广义胞映射法程序对若干非线性化学动力学模拟系统的演化过程，内在机制和全局性态进行了数值计算和分析。结果表明：胞映射方法在普适性和定量性方面表现出很好的解析功能，能够从复杂动力学系统中提取其他方法无法获取的分形结构，化学混沌，演化模式和稳定性特征，从而有助于揭示复杂非线性化学体系深层次的内在规律和机制。     

两自由度齿轮传动系统全局动力学研究

齿侧间隙的存在,使齿轮传动系统存在着丰富的非线性动力学行为.考虑两自由度齿轮传动系统的动力学模型,利用数值方法分析系统的分岔和混沌动力学行为.通过简单胞映射方法对非线性齿轮系统进行全局分析,得到系统的吸引子,吸引域等全局特性.结果显示:随着激振频率的变化,系统存在多个周期解共存以及周期解与混沌运动共存现象.最后利用系统的相轨线图与庞加莱截面图进行对比分析,在不同的初值条件下,系统呈现出不同的周期运动或混沌运动.利用简单胞映射方法的数值计算结果可以实现在不良参数条件下,通过合理控制系统的初值条件而获得理想的系统响应.     

宽带随机激励下单自由度双边非对称碰撞振动系统的稳态响应

本文以一类单自由度双边非对称碰撞振动系统为研究对象,采用广义Hertz接触模型表示碰撞过程,考察系统在宽带随机激励下的稳态响应.应用基于广义谐和函数的随机平均法推导出系统在宽带随机外激励下的伊藤随机微分方程,通过求解相应的稳态FPK方程,得到系统关于幅值、能量和位移的稳态概率密度以及位移与速度的联合稳态概率密度.另外,将系统的随机响应近似为马尔可夫过程,利用广义胞映射法得到系统的近似稳态响应.最后通过与蒙特卡罗模拟结果的对比,验证了随机平均法和广义胞映射法的有效性.     

胞映射方法研究三峡库区流域富营养化污染的演化性态

用胞映射方法对两种流域富营养化污染非线性简化系统的演化过程和全局性态进行了数值仿真、分析和探讨，结果表明：胞映射方法在解决流域时空混沌问题时表现出良好的解析能力，可从复杂动力学系统中提取常规方法无法获取的混沌形态、演化模式、奇异吸引域和吸引子特征，有助于深层次上认识和揭示复杂水域富营养化污染体系的演变过程和产生混沌的原因，为三峡库区富营养化污染的趋势预报和调控机制的研究提供新思路和实现技术。     

融合Hénon映射和元胞自动机的图像加密算法

为增强数字图像在通信传输中的安全性,提出了一种结合了 Hénon映射和元胞自动机优良特性的图像加密算法.该算法先将明文图像转换为二进制矩阵,根据外部密钥使用Hénon映射采取逐级迭代法产生伪随机序列,依据伪随机序列采用初等元胞自动机演化规则对图像信息逐行逐列地进行扩散,迭代3次后得到加密图像.经过仿真实验表明,该图像加...     

含指数积分型阻尼和周期激励系统的稳态随机响应分析

运用基于短时高斯逼近的广义胞映射方法,研究了含指数积分型非粘性阻尼和周期激励系统在高斯白噪声作用下的稳态响应.首先介绍了方法的实施过程,并推导了系统的矩方程.然后给出了系统的稳态概率密度函数,分析了阻尼系数和松弛参数对稳态响应的影响,并通过直接Monte Carlo模拟的结果验证了广义胞映射方法的有效性.     

Courbage神经元映射模型的随机共振研究

采用神经元二维映射模型,通过数字仿真研究了高斯白噪声对神经元非线性动力学特性的影响.研究发现,噪声可以诱导具有次阈值输入信号的神经元产生动作电位和随机共振.随机共振现象的产生与否和噪声强度的大小以及输入信号的频率具有密切的关系.另外,还研究了系统的控制参数对随机共振现象的影响.     

遥操作旋转运动梁系统多目标优化控制研究

本文以旋转运动柔性梁为对象,采用基于胞映射的多目标优化方法进行遥操作系统双边控制研究.首先建立遥操作旋转运动柔性梁系统动力学方程,其次考虑信号传输时滞和系统主从端跟踪误差信号设计主端控制器和从端控制器,并利用Lyapunov稳定性理论获得保证闭环控制系统稳定的控制增益所需要满足的条件.由于满足稳定性条件并不意味着好的控制性能,最后利用基于胞映射的多目标优化方法进行优化控制设计,得到同时满足多个不同目标的控制增益的Pareto最优解集.仿真结果表明所获得的控制增益能够有效实现遥操作系统主从端的信号跟踪,并且操作者能够及时感受到从端环境的变化.     

Stability preserving mappings for stochastic dynamical systems

We first formulate a general model for stochastic dynamical systems that is suitable in the stability analysis of invariant sets. This model is sufficiently general to include as special cases most of the stochastic systems considered in the literature. We then adapt several existing stability concepts to this model and we introduce the notion of stability preserving mapping of stochastic dynamical systems. Next, we establish a result which ensures that a function is a stability preserving mapping, and we use this result in proving a comparison stability theorem for general stochastic dynamical systems. We apply the comparison stability theorem in the stability analysis of dynamical systems determined by Ito differential equations     

A stochastically averaged optimal control strategy for quasi-Hamiltonian systems with actuator saturation

A stochastic optimal control strategy for quasi-Hamiltonian systems with actuator saturation is proposed based on the stochastic averaging method and stochastic dynamical programming principle. First, the partially completed averaged Itô stochastic differential equations for the energy processes of individual degree of freedom are derived by using the stochastic averaging method for quasi-Hamiltonian systems. Then, the dynamical programming equation is established by applying the stochastic dynamical programming principle to the partially completed averaged Itô equations with a performance index. The saturated optimal control consisting of unbounded optimal control and bounded bang-bang control is determined by solving the dynamical programming equation. Numerical results show that the proposed control strategy significantly improves the control efficiency and chattering attenuation of the corresponding bang-bang control.     

一种基于随机平均的最优时滞控制方法

基于时滞系统的随机平均法与随机动态规划原理,提出一种非线性系统的随机最优时滞控制方法．先应用时滞随机平均法,将非线性系统的随机最优时滞控制问题变换成非时滞的最优控制问题;再根据随机动态规划原理,建立其动态规划方程;由此确定最优时滞控制律;最后,通过一个例子说明该时滞控制方法的控制效果．     

Probabilistic solutions of some multi-degree-of-freedom nonlinear stochastic dynamical systems excited by filtered Gaussian white noise

In this paper, the state-space-split method is extended for the dimension reduction of some high-dimensional Fokker–Planck–Kolmogorov equations or the nonlinear stochastic dynamical systems in high dimensions subject to external excitation which is the filtered Gaussian white noise governed by the second order stochastic differential equation. The selection of sub state variables and then the dimension-reduction procedure for a class of nonlinear stochastic dynamical systems is given when the external excitation is the filtered Gaussian white noise. The stretched Euler–Bernoulli beam with hinge support at two ends, point-spring supports, and excited by uniformly distributed load being filtered Gaussian white noise governed by the second-order stochastic differential equation is analyzed and numerical results are presented. The results obtained with the presented procedure are compared with those obtained with the Monte Carlo simulation and equivalent linearization method to show the effectiveness and advantage of the state-space-split method and exponential polynomial closure method in analyzing the stationary probabilistic solutions of the multi-degree-of-freedom nonlinear stochastic dynamical systems excited by filtered Gaussian white noise.     

Stabilization in probability and mean square of controlled stochastic dynamical system with state delay

Although stochastic dynamical systems have received a great deal of attention in terms of stabilization studies, so far there are few works on controlled stochastic dynamical systems with state delay. In this paper, a controlled stochastic dynamical system represented by a stochastic differential equation with state delay is considered. Condition under which the system is exponentially stable in mean square and in probability is examined.     

高阶Julia集的两种生成方法及特点分析

计算机图形可视化的发展,使Julia集分形图成了研究复动力系统的一种有力工具。该文将二次复映射f（z）＝z2＋c在动态平面上拓广到高阶复映射f（z）＝zn＋c,分别给出了高阶Julia集的两种生成方法：逃逸时间算法和随机反函数迭代算法,并对两种算法的适用范围、图形性质、生成速度等特性进行了对比。     

Stochastic distribution synchronization and pinning control for complex heterogeneous dynamical networks

This paper investigates the stochastic synchronization and pinning control in the sense of probability distribution for a general model of complex heterogeneous dynamical networks subjected to stochastic disturbances. Some generic stochastic synchronization criteria are established for both cases of undirected and directed topology by using the ergodic theory on stochastic dynamical systems. Compared with most existing studies on the stochastic synchronization in the sense of mean square, it is demonstrated that the concept of stochastic distribution synchronization can well characterize the realistic structure and essential nature of complex practical stochastic systems. Subsequently, two representative examples of complex heterogeneous dynamical networks, namely coupled stochastic Duffing oscillators and coupled FitzHugh‐Nagumo neuron oscillators, are given to illustrate and numerically verify the theoretical results.     

乘性随机离散系统的最优控制

基于对系统随机不确定因素的分析,文中定义了一种新型随机离散系统--乘性随机 离散系统,并研究该类系统的线性二次型(LQ)最优控制问题.首先给出了该类系统的有限时间 和无限时间LQ最优控制律,并着重分析、证明了无限时间LQ最优控制问题的Riccati方程的 正定矩阵解的存在性及相应数值求解算法与收敛性,以及闭环系统的稳定性等问题.仿真结果 表明了该方法的有效性.     

Probability‐weighted nonlinear stochastic optimal control strategy of quasi‐integrable Hamiltonian systems with uncertain parameters

The nonlinear stochastic optimal control problem of quasi‐integrable Hamiltonian systems with uncertain parameters is investigated. The uncertain parameters are described by using a random vector with λ probability density function. First, the partially averaged Itô stochastic differential equations are derived by using the stochastic averaging method for quasi‐integrable Hamiltonian systems. Then, the dynamical programming equation is established based on stochastic dynamical programming principle. By minimizing the dynamical programming equation with respect to control forces, the optimal control forces can be derived, which are functions of the uncertain parameters. The final optimal control forces are then determined by probability‐weighted average of the obtained control forces with the probability density of the uncertain parameters as weighting function. The mean control effectiveness and mean control efficiency are used to evaluate the proposed control strategy. The robustness of the proposed control is measured by using the ratios of the variation coefficients of mean control effectiveness and mean control efficiency to the variation coefficients of uncertain parameters. Finally, two examples are given to illustrate the proposed control strategy and its effectiveness and robustness. Copyright © 2014 John Wiley & Sons, Ltd.     

Domain of stability of synchronous generators by a cell mapping approach

In this paper, the theory of simple cell mapping is applied to the determination of domains of stability of synchronous generators. The generators are represented by two-dimensional differential dynamical systems including the effects of variable damping and saliency. First, the differential equation governing the behaviour of a generator is reduced to a cell-to-cell mapping. A scheme of compactification is introduced in order to obtain a complete cell state space which consists of a finite number of cells. The methodology of the simple cell mapping is then used to prepare a computer program. Using the program, all the singularities of the cell mapping and the domain of stability can be determined readily. The method is particularly attractive because it can easily take care of any non-linearity. Different systems can be treated by the same program by simply changing the form of the differential equation in the program and/or changing the system parameters. Three kinds of synchronous machine are studied in this paper to show the applicability of this approach. The results are compared with the best of those obtained by the Lyapunov method. It is seen that almost the complete domains of stability are obtained by the new approach, including those portions which are not discovered by the Lyapunov method.