A SPECTRUM OF LYAPUNOV EXPONENTS OBTAINED FROM A CHAOTIC TIME SERIES

A complete spectrum of Lyapunov exponents (LEs) is obtained from 1970— 1985 daily mean pressuremeasurements at Shanghai by means of a correlation matrix analysis technique and it is found that there exist LEs≥0,and <0. with their sum 0λ_i=K=0.110405 whereuponT=1 /K =9 is obtained as the predictable time scale, a result close to that acquired by the dynamic-statistical approachin early days and also in agreement with that present by the authors themselves(1991).     

一类非线性时变时滞随机大系统的稳定性

讨论了线性时滞随机系统平凡解的 几乎必然渐近稳定性&并推广到非线性 多时滞随机大系统的几乎必然渐近稳定 性''提出了非线性多时滞随机大系统几 乎必然渐近稳定性的代数判据''最后&用 仿真例子说明了主要结果的可行性与有 效性     

高阶非线性系统自适应模糊有限时间状态约束控制

针对一类具有状态约束的非严格反馈高阶非线性系统,研究一种自适应模糊有限时间跟踪控制问题.首先,利用模糊逻辑系统逼近不确定性非线性函数,在此基础上,采用障碍Lyapunov函数,解决状态约束问题,通过障碍加幂积分方法和反步递推技术,提出了一种有限时间控制设计方法.在有限时间Lyapunov稳定意义下,严格证明闭环系统半全局实际有限时间稳定且系统的状态不超出给定的约束边界,并实现了有限时间跟踪控制目标.最后,仿真研究进一步验证了所提出控制方法的有效性.     

混沌系统单变量可预报性研究

对于n维的混沌系统, 不同变量的可预报性是不同的。为了研究混沌系统中单个变量的可预报性, 本文在以前提出的混沌系统整体的非线性局部Lyapunov指数基础上(李建平等, 2006), 引入了单变量的非线性局部Lyapunov指数及其相关统计量, 进一步完善了非线性误差增长理论。通过应用到几个混沌个例, 结果表明单变量的非线性局部Lyapunov指数及其相关统计量可以用来定量地研究多维混沌系统中不同变量的可预报性, 系统不同变量的可预报性之间不是相互独立的, 而是单个变量的可预报期限与系统整体的可预报期限之比都近似保持一个常数, 但各个变量的常数值有所不同。     

Influence of Sea Surface Temperature on the Predictability of Idealized Tropical Cyclone Intensity

The role of sea surface temperature (SST) forcing in the development and predictability of tropical cyclone (TC) intensity is examined using a large set of idealized numerical experiments in the Weather Research and Forecasting (WRF) model. The results indicate that the onset time of rapid intensification of TC gradually decreases, and the peak intensity of TC gradually increases, with the increased magnitude of SST. The predictability limits of the maximum 10 m wind speed (MWS) and minimum sea level pressure (MSLP) are ~72 and ~84 hours, respectively. Comparisons of the analyses of variance for different simulation time confirm that the MWS and MSLP have strong signal-to-noise ratios (SNR) from 0-72 hours and a marked decrease beyond 72 hours. For the horizontal and vertical structures of wind speed, noticeable decreases in the magnitude of SNR can be seen as the simulation time increases, similar to that of the SLP or perturbation pressure. These results indicate that the SST as an external forcing signal plays an important role in TC intensity for up to 72 hours, and it is significantly weakened if the simulation time exceeds the predictability limits of TC intensity.     

基于障碍李雅普诺夫函数非线性系统的死区补偿控制

本文集中在带有部分状态约束的非线性单输入单输出系统的自适应控制器设计上.考虑了非对称死区的非线性输入特性,选取障碍李雅普诺夫函数用来阻止部分受约束的状态违反约束条件.根据障碍李雅普诺夫函数反步法,解决了该类系统的输出跟踪问题,同时也处理了死区非线性带来的影响.针对下三角结构的非线性系统,设计了自适应控制器,证明了闭环系统所有信号都是有界的,同时保证了系统输出可以跟踪上参考信号.最后,仿真结果表明了所提方法的有效性.     

变形系统的混沌化研究

变形体变形系统是一个动态的非线性复合系统.变形运动的混沌行为验证主要通过计算系统的Lyapunov指数的正负得出.本文通过对变形系统的动力方程的混沌化研究,验证了当系统为单一连续时间系统时,构造合适的状态矩阵,保证其特征值大于某一参数就能确保变形系统的混沌化,而如果系统是反馈系统,合理选择反馈参数一样能使系统走向混沌.     

Data assimilation (4D-VAR) to forecast flood in shallow-waters with sediment erosion

In this paper, the four-dimensional variational data assimilation technique (4D-VAR) is presented as a tool to forecast floods. Our study is limited to purely hydrological flows and supposes that the weather, here a big rain, has been already forecasted by meteorological services. The technique consists in minimizing, in the sense of Lagrange, the cost function: a measure of the difference between calculated data and available observations, here the water level. This is done under constraints that are the equations of the physical model. In our case, we modified the shallow-water equations to include a simplified sediment transport model. The steepest descent algorithm is then used to find the minimum. This is made possible because we can compute analytically the gradient of the cost function by using the adjoint equations of the model. As an application of the 4D-VAR technique, the overflowing of the Chicoutimi River at the Chute-Garneau dam, during the 1996 flood, is investigated. It is found that the 4D-VAR method reduces the error in the water height forecast even when the erosion model is not activated. In terms of Lyapunov exponents, we estimate the predictability horizon of such an event to be about half-an-hour after a big rain. However, this limit of predictability can be increased by using more observations or by using a finer computational grid.     

Generalisation of a Nonlinear Dynamo Model

In order to gain a better understanding of the physical processes underlying fast dynamo action it is instructive to investigate the structure of both the magnetic field and the velocity field after the dynamo saturates. Previously, computational results have been presented (Cattaneo, Hughes and Kim, 1996) that indicate, in particular, that Lagrangian chaos is suppressed in the dynamical regime of the dynamo. Here we extend their model by removing the assumption of neglecting the inertial term. This allows for an investigation into the effect of this term on the evolution of the dynamo via a comparison of the two models. Our results indicate that this term plays a crucial role in the physics of the dynamo.     

At‐a‐station hydraulic geometry relations, 1: theoretical development

This paper, the first of two, hypothesizes that: (1) the temporal variation of stream power of a river channel at a given station with varying discharge is accomplished by the temporal variation in channel form (flow depth and channel width) and hydraulic variables, including energy slope, flow velocity and friction; (2) the change in stream power is distributed among the changes in flow depth, channel width, flow velocity, slope, and friction, depending on the boundary conditions that the channels has to satisfy. The second hypothesis is a result of the principle of maximum entropy and the theory of minimum energy dissipation or its simplified minimum stream power. These two hypotheses lead to families of at‐a‐station hydraulic geometry relations. The conditions under which these families of relations can occur in the field are discussed. Copyright © 2007 John Wiley & Sons, Ltd.