混沌的

When we put a small piece of alum into muddy water, we can see thealum can soon make the water clear.

把一小块明矾放入混沌的水中，我们发现，水很快就澄清了。

In Chapter 1, a brief reviews of bifurcation theories and chaos theory for flows and maps are presented.

第一章是关于动力系统的局部分支与混沌的预备知识。简要地介绍连续动力系统和离散动力系统的各种局部分支理论，同时对混沌的一些定义、特征及相关的判别方法也给出简要的介绍。

In chapter 3, some features of chaos and bifurcation are analyzed from the viewpoint of automatic control.

由于控制领域混沌的研究尚处于起步阶段，有许多问题需要人们去认识和解决。

Synchronization and control of chaos in nonlinear system is studied in this paper.

本文研究了非线性系统中混沌的同步化与控制问题。

Based on the equilibrium equation of an arch element the cubic nonlinear dynamic model with second order is established and the nonlinear differential dynamic system without constant term is obtained through a transfer process of T=U+b. Hence three fixed points and the homoclinic orbits are found. The critical condition of the chaotic vibration of the elastic arch is given by using the method of Melnikov function. The numerical results of the stationary and chaotic motion are given and discussed.

首先利用拱的单元平衡方程建立了拱的二阶三次非线性动力学模型；然后通过变换使方程转化为不含常数项的非线性微分动力系统，并由此得到无扰动系统的3个不动点与同宿轨道；再用Melnikov函数法给出了发生混沌的临界条件；最后给出了该系统出现定常运动和混沌运动的数值结果。

By measuring the distance between the stable manifold and the unstable manifold of the hyperbolic fixed point in the Poincare map, it is shown whether the system has transversaUy homoclinicpoints and chaos in the sense of Smale horseshoes.

Melnikov方法是用来判定一个系统是否存在Smale马蹄意义下的混沌的一种有效的数学方法，它通过测量Poincare映射的双曲不动点的稳定流形与不稳定流形之间的距离来判定系统横截同宿点的存在性及Smale马蹄意义下的混沌的存在性。

A delayed system as an infinite dimensional system can perform hyperchaotic behavior, which makes the signals hard to decipher, and new research area is developed.

而时延系统作为无穷维的系统，简单的时延系统就能够产生超混沌的特性，大大增加了破译的难度，从而开辟了混沌同步保密研究的新方向。

Then, according to phase space reconstruct technique from one-dimensional and multi-dimensional time series, the quantitative criterion and rule of system chaos which combine neural network, analyses, computations and sort are conducted on EEG signals of five kinds of human consciousness activities. The author finds that statistic results of the determinism computation in time series indicate that chaos characteristic may lie in human consciousness activities, and central tendency measure is consistent with phase graph, so it may become one division way of attractor; approximate entropy of different subjects exists discrepancy; correlation dimension and Lyapunov exponent of different consciousness activities indicate that attractors of human activities are all fractional; nonlinear quantitative criterion and rule, which unites neural network, can distinguish different styles of consciousness activity in principle, and the result of sortation takes on that consciousness activity type of arithmetic is distinguished more easily than that of abstract.

采用一维与多维时间序列相空间重构技术和系统混沌的定量判据准则，结合神经网络，对五种思维作业方式的脑电信号进行了分析、计算与分类，发现确定性计算的统计结果表明人类的意识活动中可能蕴含混沌特性，中心趋向测量(Central Tendency Measure，CTM)与相图吻合较好，可作为EEG吸引子的区分方法之一；功率谱分析反映出单个受试者的各种意识形态的差异很小，但是不同意识活动谱中的活跃频段还是略有差异的；个体之间的近似熵存在差异，同种状态下近似熵大的人可能具有更好的创新性；关联维数和Lyapunov指数的计算结果表明大脑的运动落在具有分维的奇怪吸引子上；非线性量化方法与神经网络相结合，可对人脑思维活动进行较好的分类，并且从分类结果来看数理计算类思维活动较抽象类思维活动有着更好的区分度。

I saw inflexible souls and chaotic bodies both--by my thought, grieving over confused youthhood of those chaotic bodies......

我想，我见了坚毅的灵魂与混沌的躯体。对於那些混沌的躯体，我悼念你们乱无章法的青春。。。。。。

"I have you both beaten," the lawyer gloated."Before Adam and Eve, before the Garden of Eden, before all creation, there was a state of chaos, and who do you think could have created that?"

&你们俩的都不如我的早，&律师得意地说：&在亚当和夏娃之前，在伊甸园之前，在所有这些创造之前，有个混沌的世界，你们知道，是谁制造了那个混沌的世界吗？&

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。