混沌

Researches show that chaotic systems have characteristics of ergodic property, non-periodicity and quasi-randomicity, so chaotic systems fit for information encryption.

但是目前研究的多数加密方案都是基于低维混沌系统，存在保密性差、易被网络重构信号等方法破解的危险，并且缺少必要的安全性分析。

By use of the orbital ergodic property of chaotic optimization and the learning, memory, association and fault-tolerant functions of artificial neutral network, the optimization of the pollutant-receiving water system in a mine reform project was made so as to effectively control the main pollutants such as COD,Pb etc.whic...

利用混沌优化的轨道遍历性和人工神经网络的学习、记忆、联想和容错性，对某矿山扩建项目中污染物的受纳水系进行优化，以有效地控制生产过程中的主要污染物如COD ，Pb等。

Numerical explorations of Henon, Lorenz and others, Mathematical works of Sinai, Bunimovich and Szasz, contributed to the development of modern ergodic theory and chaotic dynamics.

Henon、Lorenz等的数值探索、Sinai、Bunimovich、Szasz等的数学理论工作对现代遍历理论和混沌的研究起了很大的作用。

In chapter 3, on the basis of measure, integration and ergodic theory, it is proved that the statistcal properties and the general complexity of the binary sequences (CG-sequences){b〓} b〓∈{1,-1} generated by a kind of chaos systems and mapping η〓 are as good as white noise sequences. These results lay the foundation of further development.

第三章运用测度、积分以及遍历理论中的一些基本原理，证明了由一类混沌差分系统和映射η〓所产生的二元序列{b〓}，b〓∈{-1，1}，具有与白噪声类似的统计特性和广义复杂度。

After introducing some basic results from ergodic theory, two probIems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system.

首先介绍了遍历理论的一些经典结果；然后着重研究了对应于混沌映射的绝对连续不变测度的存在性与计算问题，这归结于相应的Frobenius-Perron算子的泛函分析与数值分析；最后《确定性系统的统计性质》介绍了Shannon熵、Kolmogorov熵、拓扑熵以及Boltzmann熵，并给出了不变测度的一些最新应用。

Jiu Ding,Aihui Zhou,Statistical Properties of Deterministic Systems Statistical Properties of Deterministic Systems discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two probIems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation.

摘要本书介绍的是确定性离散动力系统统计性质的基本理论与计算方法，首先介绍了遍历理论的一些经典结果；然后着重研究了对应于混沌映射的绝对连续不变测度的存在性与计算问题，这归结于相应的Frobenius—Perron算子的泛函分析与数值分析；最后本书介绍了Shannon熵、Kolmogorov熵、拓扑熵以及Boltzmann熵，并给出了不变测度的一些最新应用。

By using the property of chaos ergodicity, a PID controller based on chaos optimization was designed.

利用混沌运动遍历性和随机性的特点，对PID控制器进行参数寻优。

By making use of the ergodicity specific to the chaotic theory, one can improve the chaotic-searching optimization method based on Logistic mapping.

在优化设计领域中，混沌现象的遍历性特点可以作为搜索过程中避免陷入局部极小的一种优化机制。

As a new optimization technique, chaos bears randomicity, ergodicity and the superiority of escaping from a local optimum.

混沌是一种新颖的优化技术，具有随机性、遍历性的特点和易跳出局部极值的能力。

As the network applies the the randomness and orbital ergodicity of chaos searching,it has higher ability of searching global optimal solutions.

网络利用了混沌搜索的随机性和轨道遍历性，因而具有较强的全局寻优能力。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。