混沌

In the first part, an ideal non-noise spatio-temporal series (33 modes Lorenz system) is used as a generator for chaotic spatio-temporal series in comparison and sensitive tests with the field time series analysis method.

在第一部分中，以一个"理想"的混沌时空序列即33模Lorenz系统，作为时空混沌序列的"发生器"，通过状态空间重构，利用场时间序列的局域近似方法建立预测模型，进行对比试验和敏感性试验。

In Chapter 4, in the above system, the definitions of sensitive dependence on initial value, strong sensitive dependence on initial value and chaos set of a sequence of maps are put forward; Meanwhile, sensitive dependence on initial value of a sequence of maps is promited, and the concept of N - sensitive factor is also proposed; That at the local connected space λ_2/(N-1) is a N—sensitive factor, and a chaotic map containing strong sensitive dependence on initial value of a sequence of maps is proved.

第四章，在上述系统中给出了一列映射的初值敏感依赖、初值强敏感依赖和混沌集的定义；同时又对一列映射的初值敏感依赖进行了推广，提出了该系统下一个N-敏感系数的概念：证明了在局部连通空间中λ_2/N-1是系统的一个N-敏感系数；又证明了一列映射的混沌集蕴涵一列映射对初始条件具有强敏感依赖性。

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。

In order to synchronize the strange nonchaotic system, contraction map is used to synchronize the chaotic driving system.

为实现两个奇异非混沌吸引子的同步，文中采用收缩映射实现混沌驱动系统的快速同步。

Realized t he chaotic sy nchronization in ac cording to e xponent st ability.

即在达到混沌同步的同时，保证了混沌系统

Firstly, Some of the basic concepts of chaotic vibration are introduced, the qualitative and quantitative methods of chaotic vibration identification are detailed, the selection of associated parameters is studied, the algorithms for calculating the maximum Lyapunov exponent, correlation dimension and periodicity ratio are provided. On the basis of analysis and comparison of different methods, the methods used in the paper are selected.

本文首先介绍了混沌振动的基本概念；评述了混沌振动识别的定性和定量方法；对有关参数的选择进行了研究；给出了计算最大Lyapunov指数、相关维数和周期比的算法；在对不同方法对比分析的基础上，选出了本文拟采用的识别方法。

Chaos theory is to explain the ubiquitous complexity in nature and the human society. What it presents is the inner randomicity character that looks like ruleless in determinate system.

混沌理论是揭示自然界及人类社会中普遍存在的复杂性的理论，混沌表现的是确定性的非线性系统的貌似无规则的内在随机性。

By utilizing the basic theory of chaos and fractal,on the basis of reading a vast amount of literatureand summing up predecessors achievements,using the three methods of analysis,computation andexperiment,this paper research for the overlapping embedment topology distribution structure of thegeneralized M-J sets and chaos phenomenon in the multi-dimension determinate nonlinear system(such as the cardiac system of species of the different level of evolution,the two-dimensional nonlinearmap,etc).

本文利用混沌与分形的基本理论，在大量阅读文献，总结前人的成果的基础上，采用解析、计算和实验三种手段并用，主要研究了广义M-J集的嵌套拓扑分布结构和多维确定性非线性系统(如进化程度不同物种的心脏系统、二维非线性映射等)中的混沌现象，取得了以下方面的创新

Because the time series generated from finite difference equation with chaos may also possess exponential distribution of probability density. Additionally, irregular dynamics has ever been attributed to the presence of stochastic noise in many systems, but actually it may result from chaotic process in deterministic system.

近年来对非线性动力系统的深入研究发现：观察到某一过程具有指数型概率密度事件分布并不足以确定它就是泊松过程，由具有混沌行为的有限差分方程所产生的时间序列也可具有指数型概率密度分布；在许多系统中，过去归因于随机噪声的不规则动力学特性，实际上很有可能是由确定性系统中的混沌过程所致。

The analysis results show the differential geometry method is effective for controlling chaos of power system and its control property is better than that of other methods.

研究表明：采用微分几何方法能够对电力系统的混沌行为进行有效控制，控制效果与其他混沌控制方法相比，具有明显的优越性。理论分析和数值仿真结果都证明了该控制方法的有效性。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。