当我在创作《混沌》的时候，圣克鲁兹动力系统集团(Dynamical Systems Collective)的年轻人曾试着给我解释克劳德·香农(ClaudeShannon)发明的信息理论。
When I was working on Chaos, the young rebels of the Dynamical Systems Collective in Santa Cruz would try to explain Claude Shannon's invention of information theory to me.
这幅图片展示了曼德尔勃特集合(Mandelbrotset)与离散混沌动力系统(logistic map)之间的一致性，这解释了复杂而无序的行为可以由简单的非线性动态方程序中得出。
This graph shows correspondence between the Mandelbrot set and the logistic map, which explains how complex, chaotic behavior can arise from simple non-linear dynamical equations.
应用先进的计算机图形学及科学计算可视化技术，编制了非线性动力系统仿真分析程序，可直观地分析混沌动力系统的轨迹特性。
This paper compiles the analysing program for the simulation of the nonlinear dynamic system. With this program, the locus property of the nonlinear dynamic system can be analysed visually.
混沌是确定系统的非线性动力系统中出现的随机现象。
Chaos is a random phenomenon in deterministic nonlinear dynamic systems.
混沌现象是非线性动力系统中一种确定的、类似随机的过程。
As a phenomenon found in non-linear dynamic system, chaos is deterministic and random-like.
为了讨论混沌运动，对一类非线性动力系统的自由振动方程进行了求解。
A kind of free vibration equation of the nonlinear dynamical system is solved to study chaotic movement.
从混沌的角度来看，随机过程的多重分形谱是动力系统的重要特征，熵率只是多重分形维中特殊的一维，即信息维。
Known from the theory of chaos, multi-fractal of stochastic process is a key characteristic of its dynamics, of which entropy rate is a special fractal dimension named information dimension.
为了研究混沌运动，对一类非线性动力系统的自由振动方程进行了求解，继之给出了单层扁锥面网壳非线性自由振动微分方程的准确解。
In order to study chaos movement, Accurate solution of non-linear free vibration differential equation is by solving a kind of free vibration equation of non-linear dynamics system.
基于动力系统模型的局部投影非线性降噪算法，对混沌信号和一大类非平稳信号具有明显的降噪效果。
The algorithm of local projective nonlinear noise reduction based on nonlinear dynamic system is more effective for noise reduction of chaotic signal and non-stationary signals.
研究了混沌动力系统的同步问题。
The issue of synchronization of chaotic dynamical systems is investigated.
最近粘性流体分布混合和动力系统的混沌行为联系起来，为分析和理解各种混合提供了新思路。
Recently, mixing of liquids has been associated with the chaotic behavior of dynamics system and it is to provide a new method for analyzing and understanding numerous mixing.
对复域混沌动力系统作出了构建示例。
Give a construct example of chaos dynamic system in complex field.
岩体混沌动力系统演化过程的可预测尺度是非线性预测理论研究的重要内容。
Predictable time scale of the evolution of chaotic rock mass dynamic systems is one of the most important parameters in nonlinear forecasting theory.
提出分形上的混沌动力系统以及混沌与神经网络相结合的方法，可为水科学问题的研究能提供一些新的思路。
Finally, we suggest that the fractal chaos dynamical system and the mean of combining chaos with neural net provide several new methods in the future studying.
提出了一种基于混沌动力系统同步原理的非对称数字水印构造方法。
A method of making an asymmetric digital watermarking based on chaotic synchronization theory is proposed in this paper.
根据股票市场是非线性动力系统的假设，利用混沌理论对混沌时间序列的分析方法，提出了股票价格预测方法。
A method of stock price prediction is presented by hypothesis of stock market being non-linear dynamic system and analyzing method of chaos theory for chaos time series in this paper.
本文讨论了符号动力系统的几乎周期点、回归点及混沌集。
Some properties of almost periodic points, recurrent points and chaotic sets in symbolic dynamical systems are given.
基于混沌动力系统相空间的延迟坐标重构和双线性表达式，设计了预测混沌时间序列的双线性自适应预测滤波器。
Based on the delay-coordinate reconstruction and bilinear expressions in the phase space of a chaotic system, a bilinear adaptive filter was designed to predict low-dimensional chaotic time series.
把对有限维离散化系统混沌控制的方法应用于高维微分动力系统，讨论了双光子光学双稳系统中的混沌控制。
Applying the method of controlling chaos presented by documents to a high dimensional differential dynamical system, the control of two photon optical bistable system's chaos is discussed.
混沌经济时间序列的预测方法研究是混沌经济非线性动力系统的重要内容。
The research on forecasting method of chaotic economic time series is the important part of the nonlinear chaotic economic dynamic systems.
研究了一类具有良好隐蔽性的一元三次离散动力系统的混沌序列产生情况，提出了混沌序列的异或和置乱加密算法。
The chaos sequence procedure of a kind of discrete dynamic system with good concealing feature is studied, and two algorithms about chaos sequence are provided.
在了解混沌非线性动力系统特征的基础上，本文就混沌非线性系统的智能控制方法进行了研究。
Based on the understanding of characters about the chaotic nonlinear dynamical systems, intelligent control methods for chaotic nonlinear systems are presented.
混沌和混沌控制是非线性动力系统的新理论、新方法和新概念，是智能控制的重要组成部分。
Chaos and control of chaos are new theory and new methodology and new concept of nonlinear dynamic system, which has become an important part of intelligent control.
本文讨论了符号动力系统子移位的弱混沌，并得到拓扑熵为零的弱混沌子移位。
In this paper, we study weakly chaos on sub-shift of symbol dynamical system, and give a weakly chaotic sub-shift whose topological entropy is zero.
神经网络是高度复杂的非线性动力系统，存在着混沌现象。
Neural network is a kind of highly complex nonlinear dynamic system, and chaotic phenomenon was found in it.
计算结果表明，该方法对高维微分动力系统中的混沌控制是有效的。
The numerical calculation shows that it is effective to use the method in the control of a high dimensional differential dynamical system.
分形几何学在图像数据压缩、模拟自然景物，艺术图案设计、分形生长及混沌动力系统的研究等方面有着广泛的应用。
Fractal is widely used in many fields such as the image data compression, simulation of natural scenery, the growing of fractal geometry and the research of chaos motility system.
动力系统的基本概念。分歧，混沌，不规则，映射。
Basic notions of dynamical systems. Bifurcations, chaos, fractals, maps...
讨论一类非线性结构动力系统混沌运动的条件。
The conditions for chaotic motions of some dynamical systems with nonlinear structures are studied in this paper.
混沌是确定性非线性动力系统内在随机性的表现。
Chaos is internal random behavior expression of certainty nonlinear dynamical system.
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