混沌

These nonlinear chaos dynamitic models forecast oil consumption quantity of China. In this dissertation, it has mainly studied the fractural dimension measure to petroleum economics system, the phase space reconstruction modeling and prediction techniques to economic chaotic time series. It puts forward chaos dynamitic models, which are forecasting model for oil consumption. Corresponding countermeasures of the oil supply-security of China are suggested by analyzing the forecasting results and the problems existing in petroleum economic system of China, especially aiming at the balance between oil production and consumption quantity.

本论文主要研究了石油经济系统复杂性的分数维度量、经济混沌时间序列的相空间重构技术、建模和预测技术；建立了石油经济系统的混沌动力学模型：石油消费的预测模型；并将此模型应用于全国的石油经济系统研究之中，对全国石油消费量做出预测，根据预测结果分析我国石油经济系统中存在的问题，并提出对策。

On the chaos correspondence question, this article proposed the implicational method of chaos system in the secure communication system.

就混沌通信问题，本文提出了有关混沌系统在保密通信系统的实现方法。

Duffing equation has parameter and initial value sensitivity. It can generate chaotic state by adjusting the parameter and initial value, and it also can generate intermissive chaotic state, if the ideal signal and the measured signal applied to the system simultaneously. The actual measured signal can be measured by using this state.

Duffing方程具有参数敏感性和初值敏感性，通过调节Duffing方程的参数和初值可以产生混沌现象，且被测信号和理想信号如果共同作用在Duffing方程上，可以产生有规律间歇混沌现象，利用这种现象就可以实现周期信号的频率测量。

Nonisotropic chaotic vibration by means of the total variation theory is characterized.

用混沌振动理论刻画非迷向混沌振动。

The boom of research on chaotic ciphers occurred from 1989, two chaotic ciphers schemes proposed by Matthews, Pecora and Carroll, respectively and much more contributions are made to get many promising achievements.

从1989年Matthews， Perora和Carroll分别提出混沌密码学中的两种方案之后，混沌密码的研究进入了繁荣时期，取得了大量的研究成果，出现了不少充满希望的进展。

The bifurcation and chaos behavior of impact and rubbing fault rotor system caused by the parameters of nonlinear rigidity, rotor rotating speed, eccentric mass is analyzed, in the numerical value analysis method. The bifurcation diagrams, maximum Lyapunov exponent diagrams, Poincaré maps, phase plane portraits, trajectories of journal center, time-history curve, amplitude spectra diagrams of the rotor motion are used. The convert and evolution course of periodical response, quasi-periodical response, double-periodical bifurcation, chaos of the system response is analyzed.(3). It is deduced that the general differential equation of bending-torsional-pendular coupling vibration about rotor with the gyroscopic moment. On the basis of this equation, the general differential equations of coupled bending, torsional and pendular nonlinear vibration about rotor with unbalance character and rubbing character are deduced.

2建立了具有非线性刚度的转子系统在非稳态非线性油膜力作用下的径向碰摩动力学微分方程，并应用含高阶余项的非线性动力方程的线性化数值法研究了此类系统响应的复杂动力学行为，利用转子响应的分岔图、最大Lyapunov指数曲线、Poincaré截面映射、时域波形、相轨线、轴心轨迹、幅值谱等图形分析了系统响应的周期运动、拟周期运动、倍周期分岔、混沌等运动形式的转化与演变过程，重点研究了非线性刚度、转子转速、偏心质量等系统参数对碰摩故障转子系统的分岔和混沌行为的影响。

In this paper, the background of fake information diffusion in public crisis management was firstly analyzed, and then three basic propositions and three hypothesis of simulation were concluded. Then, the management countermeasures of fake information diffusion in public crisis were classified as fifteen types according to the types of strategy and executive ability, and then fifteen corresponding simulation schemes were put forward. Meanwhile, a management simulation model of fake information diffusion in public crisis was constructed and used to phenomenologically simulate the scenarios and validity of five among these fifteen management countermeasures. At last, these simulation results were contrasted and analyzed, and five novel but meaningful conclusions were drawn.

首先对公共危机伪信息特殊性及其管理复杂性进行分析，得出论文研究的三大基本命题与三大研究假设；在此基础上，一方面分析了混沌理论方法在公共危机伪信息管理仿真中的适用性，并根据混沌情景预测方法构建了公共危机伪信息扩散的管理仿真模型，另一方面依据所提出的基本命题与研究假设，从管理策略与管理执行力度两方面对公共危机伪信息管理模式进行分类，形成了十五个仿真方案；最后利用所构建的仿真模型其中的五个仿真方案的管理绩效与扩散情景进行唯象仿真，并对仿真结果进行横向对比分析，得出五大结论。

Simulation results validate the proposed synchronization methods and show its robusticity.

数值仿真结果表明，所设计的混沌控制器能有效的实现混沌同步，并且具有很强的鲁棒性。

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。

Though the timing-translocation graph Poincare graph power chart judgechaos, summering the regulation of duffing equation emerging chaos.

通过时程曲线、相平面图、蓬加莱映射、功率谱、分岔图来判断混沌现象，归纳了一类非线性振动系统方程的一些出现混沌现象的规律。

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。