Characteristics Of Chaotic Attractors In Atmospheric Boundary-Layer Turbulence

In this paper, the attractors of turbulent flows in phase space are reconstructed by the time delay technique using observed data of atmospheric boundary-layer turbulence, which include high resolution temperature, humidity andthree-dimensional wind speed measurements in Gansu province and Beijing, China. The correlation dimensions and largest Lyapunov exponents have been computed. The results indicate that all the largest Lyapunov exponents in different conditions of time, site and atmospheric stability are greater than zero. This means that the atmospheric boundary-layer turbulence system is really chaotic and has appropriate low-dimensional strange attractors whose dimension numbers range from 3 to 7 and vary with different variables (dynamical variables or non-dynamical variables) and atmospheric stability. Turbulent kinetic energy is first applied to reconstruct the attractor of turbulence, and is found to be feasible.     

Lyapunov 指数预报模式

考虑到系统在吸引子附近的演化行为是指数辐散的，我们把浑沌理论和统计原理相结合，提出了Lyapunov指数预报模式。个例试验的结果是令人满意的。     

地震道的非线性混沌反演——Ⅰ.理论和数值试验

全文以地震道反演的数值实验为例,根据混沌理论讨论了非线性地震反演的以下特性:1.对于带误差的地震数据和极其平滑的初始模型,逐次线性化的迭代过程产生的输出序列最终走向无序,这是非线性反演系统本身的特性决定的;2.迭代（非线性反演）系统是由Poin-care映的或系统方程描述的;3.可以根据地震反问题的特点,用多种不同的方法定义相应的Lyapunov指数,它们的数值和组合是非线性反演系统状态的有效指示;4.取决于系统参数的选取,发现在二维相空间有奇异吸引子的对应物.总之,从混沌理论的角度来研究纯数学的非线性地震反问题,可以揭示某些过去鲜为人知的内在规律性.本文为全文的上篇,主要讨论前两个问题,即理论和地震道反演数值试验结果.     

非线性地震道的混沌反演——Ⅱ.关于Lyapunov指数和吸引子

在本文上篇《非线性地震道的混沌反演——1.理论和数值试验》中讨论了非线性反问题逐次线性化方法及迭代过程的系统特性、递推法和广义线性反演法输出波阻抗序列的特征。本篇参照混沌理论中关于Lyapunov指数、相空间和吸引子的概念,深入研究逐次线性化迭代的状态变化的阶段性及其定量描述.当引用相空间描述系统的演化时,对于随迭代变化的阻尼因子可以发现几种吸引子.最后,总结了非线性地震混沌反演的要点,指出非线性反演迭代的复杂阶段性要川混沌理论来描述,而Lyapunov指数等才是控制迭代过程的实质性参数.     

Least squares parameter estimation in chaotic differential equations

A recent least squares algorithm, which is designed to adapt implicit models to given sets of data, especially models given by differential equations or dynamical systems, is reviewed and used to fit the Hénon-Heiles differential equations to chaotic data sets.This numerical approach for estimating parameters in differential equation models, called theboundary value problem approach, is based on discretizing the differential equations like a boundary value problem,e.g. by a multiple shooting or collocation method, and solving the resulting constrained least squares problem with a structure exploiting generalized Gauss-Newton-Method (Bock, 1981).Dynamical systems like the Hénon-Heiles system which can have initial values and parameters that lead to positive Lyapunov exponents or phase space filling Poincaré maps give rise to chaotic time series. Various scenarios representing ideal and noisy data generated from the Hénon-Heiles system in the chaotic region are analyzedw.r.t. initial conditions, parameters and Lyapunov exponents. The original initial conditions and parameters are recovered with a given accuracy. The Lyapunov spectrum is then computed directly from the identified differential equations and compared to the spectrum of the true dynamics.presently at IWR, Universität Heidelberg, Im Neuenheimer Feld 368, D-6900 Heidelberg, Germany     

深埋隧道围岩系统卸荷演化过程的Lyapunov指数分析

岩石材料本质上是一种物理非线性的材料,在深埋条件下,隧道围岩系统的变形还表现出几何非线性,这两种非线性机制的相互作用使得围岩系统的卸荷演化具有高度的复杂性.根据重庆某深埋隧道围岩实际情况,运用FLAC3D三维显式有限差分法分析软件,建立了摩尔-库仑剪破坏与拉破坏复合的应变软化模型,采用大变彤方法对深埋隧道围岩系统卸荷进行数值仿真,引入混沌动力学理论对数值模拟的分析结果进行整合,提取了围岩系统演化过程中特征点演化时间序列的Lyapunov指数,对其混沌形态进行了研究.实例分析表明:深埋隧道围岩系统卸荷演化呈现典型的混沌性态,且系统演化具有对初始条件的敏感性.     

具有单向强耦合的时滞大系统的稳定性

针对具有单向强耦合的时滞大系统,通过构造Lyapunou泛函,并采用部分分解法,给出了判定系统一致渐近稳定的充分条件。与传统的分解等价法相比,该方法扩大了单方向关联项的界限,并可通过参数的选取扩大时滞界限,结论易于验证,具有实际应用价值。     

Research on the Stability of the Circular Restricted Three-body Problem with Radiation and Oblateness

The velocity scaling factor method based on the least squares principle is regarded as the most efficient, stable, and widely-used method among all the manifold correction methods. The stability of the restricted three-body problem where the primary body is a source of radiation and the secondary body is an oblate spheroid is discussed by using the velocity scaling factor method. The numerical simulations suggest that (1) the number of the chaotic orbits will increase if only the oblate spheroid perturbation is considered; (2) the number of the regular orbits will increase if only considering the radiation pressure; (3) when both the radiation and oblateness perturbation exist, the radiation plays a dominant role, and the probability of regular motion of the system will increase.     

Eddy-induced cross-shelf phytoplankton transport along the downwelling coast off Western Australia

Along the downwelling coast off Western Australia, late-autumn/early-winter chlorophyll a blooms are observed on the continental shelf south of Shark Bay (26°S), in contrast with summer blooms in the north. The late-autumn/early-winter blooms are in phase with seasonal strengthening of the Leeuwin Current and its eddy field. Anticyclonic eddies entrain the high phytoplankton biomass waters from the shelf and transport offshore into the oligotrophic, subtropical marine environment, as revealed by coalescing the finite-size Lyapunov exponent (FSLE) of the surface geostrophic flow field and the satellite chlorophyll a images.     

基于相空间重构的边坡位移预测

根据边坡位移时间序列的非线性性质, 应用基于相空间重构的实时预测方法, 可以充分利用时间序列信息, 预测 各种边坡变形演化趋势。 讨论了局域法和基于 Ly apunov 指数的预测法。 实例研究表明, 基于相空间重构的预测方法具 有比非平稳时间序列更高的预测精度和更广的适应性。