极坐标系下移动机器人的点镇定

研究由动力学模型描述的轮式移动机器人的点镇定问题。首先建立极坐标系下系统方程,进而给出运动学控制器设计方法,再结合系统的动力学特性,利用Lyapunov方法和反步法将运动学控制器拓展到动力学,最终设计出光滑的控制律并保证系统变量渐近收敛到零。仿真结果表明该方法的可行性和有效性。     

on the relationship between fast lyapunov indicator and periodic orbits for symplectic mappings

The computation on a relatively short time of a quantity, related to the largest Lyapunov Characteristic Exponent, called Fast Lyapunov Indicator allows to discriminate between ordered and weak chaotic motion and also, under certain conditions, between resonant and non resonant regular orbits. The aim of this paper is to study numerically the relationship between the Fast Lyapunov Indicator values and the order of periodic orbits. Using the two-dimensional standard map as a model problem we have found that the Fast Lyapunov Indicator increases as the logarithm of the order of periodic orbits up to a given order. For higher order the Fast Lyapunov Indicator grows linearly with the order of the periodic orbits. We provide a simple model to explain the relationship that we have found between the values of the Fast Lyapunov Indicator, the order of the periodic orbits and also the minimum number of iterations needed to obtain the Fast Lyapunov Indicator values.     

FAST LYAPUNOV INDICATORS. APPLICATION TO ASTEROIDAL MOTION

We present a very simple and fast method to separate chaotic from regular orbits for non-integrable Hamiltonian systems. We use the standard map and the Hénon and Heiles potential as model problems and show that this method appears to be at least as sensitive as the frequency-analysis method. We also study the chaoticity of asteroidal motion. This revised version was published online in July 2006 with corrections to the Cover Date.     

一类变系数非线性时滞微分系统的全局指数稳定性

通过构造Lyapunov函数,并应用一类时滞微分不等式,研究了一类交系数非线性时滞微分系统的全局指数稳定性,得到若干判定条件,推广了一些文献的结果。     

海洋温度场稳定性与可预报性研究

海洋温度场具有强烈的时空易变性,带有典型的混沌特征,研究其稳定性对改善温度场可预报性具有重要意义。以混沌理论为支撑,改进最大Lyapunov指数算法,基于POM数值模式预报的温度时序为试验样本,研究了东中国海范围内的海洋温度场混沌稳定性分区和特征,并在此基础上针对混沌强弱区做添加观测试验,研究了基于稳定性分区的温度场可预报性。仿真结果表明,在混沌强烈区添加观测相比较弱区对改进预报效果更显著,对混沌强烈区添加观测整体上可以降低预报温度均方根误差0.2~0.7℃左右,证实了在该区域加强观测能在一定程度上改善温度场的可预报性。     

基于混沌时间序列的地下水位多步预测模型

利用相空间重构技术,并借助G-P算法、C-C方法和Wolf方法从宁陵地区地下水位一维时间序列中提取Lyapunov指数,结果表明此时间序列具有混沌特征。计算了宁陵地区地下水位时间序列的关联维数、时间延迟和最大Lyapunov指数,将局域加权一阶多步预测模型应用于地下水位预测。预测表明,此模型可有效应用于地下水位时间序列的多步预测。     

On the Stochasticity of the Asteroid Belt

The study of the stochasticity of the asteroid belt requires the analysis of a large number of orbits. We detect the dynamical character of a set of 5 400 asteroids using the Fast Lyapunov Indicator, a method of analysis closely related to the computation of the Lyapunov Characteristic Exponents, but cheaper in computational time. For both regular and chaotic orbits we try to associate the motion to the underlying resonances network. For it we consider different methods of classification of rational numbers proposed by number theory, and we choose the one which seems to be strictly related to the dynamical behaviour of a system. This revised version was published online in July 2006 with corrections to the Cover Date.     

一类基因调控网络的定性分析

运用巴拿赫压缩映像原理讨论了一类由微分方程描述的具有SUM逻辑的 基因调控网络平衡位置的存在唯一性,并结合基因调控网络的实际背景,分析 了基因调控网络平衡位置的Lyapunov稳 定性,获得若干充分条件     

变形监测数据的混沌现象分析

简要介绍了识别变形数据混沌现象的Lyapunov指数方法和关联维数方法;讨论了变形监测数据的Lyapunov指数和关联维数的计算方法;最后结合大坝观测变形观测数据给出了实际算例。     

The Phase Space Structure Around L4 in the Restricted Three-Body Problem

The phase space structure around L ₄ in the restricted three-body problem is investigated. The connection between the long period family emanating from L ₄ and the very complex structure of the stability region is shown by using the method of Poincarés surface of section. The zero initial velocity stability region around L ₄ is determined by using a method based on the calculation of finite-time Lyapunov characteristic numbers. It is shown that the boundary of the stability region in the configuration space is formed by orbits suffering slow chaotic diffusion.