南沙群岛海域近海面大气湍流混沌特性

混沌概念的提出,有必要研究大气湍流是否具有混沌行为。根据1994年9月18—30日南沙群岛海域渚碧礁（10°52＇N,114°04＇E）的近海面大气水平风速及气温的观测资料,计算和分析了有关诊断系统是否是混沌运动的特征量：关联维数、Lyapunov指数和关联熵。结果表明,南沙群岛海域近海面大气湍流是一种混沌运动。同时给出并讨论了其它一些结论。     

Practical control of underactuated ships

This paper presents a design of global smooth controllers that achieve the practical stabilization of arbitrary reference trajectories, including fixed points and nonadmissible trajectories for underactuated ships. These ships do not have an independent actuator in the sway axis. The control design is based on several nonlinear coordinate changes, the transverse function approach, the back-stepping technique, the Lyapunov direct method, and utilization of the ship dynamics. Simulation results illustrate the effectiveness of the proposed control design.     

非线性误差增长理论在大气可预报性中的应用

为了能从非线性误差增长动力学的角度来研究大气的可预报性问题,在非线性动力系统的理论和方法基础上,文中引入了可预报性研究的新方法--非线性局部Lyapunov指数.非线性局部Lyapunov指数及其相关统计量能够用来定量地确定混沌系统可预报性的大小,真正地实现了对可预报性的定量化研究.首先给出了利用大气单个变量的实际观测资料获得其可预报期限估计的计算方法,因而解决了将非线性误差增长理论应用到大气实际的可预报性研究中的问题.然后,以位势高度场为例,详细讨论了逐日时间尺度上全球可预报性的时空分布,得到的主要结论为:(1)在水平方向上,全球位势高度场可预报性表现为一定的南北纬向带状分布,赤道地区和南极地区的可预报期限最长,可以达到两周左右;北极地区次之,可预报期限大约为9-12 d;北半球中高纬度地区可预报期限相对较短,可预报期限大约为6-9 d;而在南半球的中纬度地区最短,可预报期限仅为4-6 d.此外,500 hPa位势高度场可预报性分市随季节有明显变化,季节不同一些可预报期限的高值区和低值区所在的纬度和经度也会不同,总体来说,全球大部分地区的可预报性冬季都大于夏季,尤其在南极地区、热带印度洋以及北太平洋地区.(2)在垂直方向上,位势高度场可预报期限随高度升商而增加,可预报期限从对流层下层的两周以下增加到平流层下层的1个月左右,对流层和平流层天气尺度运动的可预报期限与其时间尺度是十分一致的.     

Lagrangian coherent structures in the California Current System – sensitivities and limitations

We report on numerical experiments to test the sensitivity of Lagrangian coherent structures (LCSs), found by identifying ridges of the finite-time Lyapunov exponent (FTLE), to errors in two systems representing the California Current System (CCS). First, we consider a synthetic mesoscale eddy field generated from Fourier filtering satellite altimetry observations of the CCS. Second, we consider the full observational satellite altimetry field in the same region. LCS are found to be relatively insensitive to both sparse spatial and temporal resolution and to the velocity field interpolation method. Strongly attracting and repelling LCS are robust to perturbations of the velocity field of over 20% of the maximum regional velocity. Contours of the Okubo–Weiss (OW) parameter are found to be consistent with LCS in large mature eddies in the unperturbed systems. The OW parameter is unable to identify eddies at the uncertainty level expected for altimetry observations of the CCS. At this expected error level, the FTLE method is reliable for locating boundaries of large eddies and strong jets. Small LCS features such as lobes are not well resolved even at low error levels, suggesting that reliable determination of lobe dynamics from altimetry will be problematic.     

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。