混沌

The riddled basins of the chaotic synchronized attractor in these two-type coupled systems are analytically proved and the stability of the chaotic synchronized attractor is also studied. In succession, the local-global riddling bifurcation is discussed.

本文首先研究了两种常见形式的一维斜帐篷映射的耦合混沌同步系统，讨论了其混沌同步状态的稳定性，解析证明其同步混沌吸引子的吸引域是筛形域。

In order to extend the effect and security of image encryption algorithm.An image encryption algorithm is presented based on three-dimension chaotic system and bit-computation.The permutation sequences and binary sequences are generated using three-dimension chaotic system.Firstly,the image is pretreated using chaotic system and permutation transformation,then the pixel's gray value's bit sequences are permuted using the permutation sequences generated before,at last,the pixel's gray value's bit sequences are computed by using XOR operating and the binary sequences.

为了改进图像加密算法的安全性和效率，提出了一种基于三维混沌系统和位运算的数字图像加密算法，利用三维混沌序列的坐标分量分别产生置换序列和二值序列，在对待加密图像进行预处理的基础上，先应用混沌置换序列对预处理的结果图像进行基于灰度值位序列的置换操作，然后再应用产生的二值序列对结果图像的灰度值位序列进行位异或加密运算。

Their influence on the chaotic motion region is also examined. With temperature rising the changes of modul of elasticity and coefficient of thermal expansion of plate will not effect chaotic motion region.

结果表明：随温度、长宽比的增加，混沌运动区域变大，随着倾斜角及板厚的增加，混沌运动区域将变小，且温度升高引起板的弹性模量及热膨胀系数的改变对混沌运动区域几乎没有什么影响

At last, the frequency spectrum analysis shows that the four-winged chaotic attractor has extremely wide frequency bandwidth compared with that of the Lorenz system and Chua circuit, which is important in practical applications in communication encryption etc.

最后，通过比较该四翼混沌吸引子的系统、Lorenz系统、Chua氏电路等混沌信号的频谱发现，四翼混沌吸引子的系统信号具有极宽的频谱带宽，该特性在通讯加密等工程应用中具有重要价值。

Chaos and Fractals, as the important fields of nonlinear system science, have been paid great attention in recent years, and a great deal of achievements has been made both in the theory and application in engineering.

混沌分形作为非线性科学研究的核心内容，近二十年来引起了人们的广泛关注，并在混沌分形理论的探讨和混沌分形工程应用等方面均取得了可喜的研究成果。

Chaos and Fractals, as the important fields of nonlinear system science, have been paid great attention in recent years, and a great deal of achievements has been made both in the theory and application in engineering.

摘要混沌分形作为非线性科学研究的核心内容，近二十年来引起了人们的广泛关注，并在混沌分形理论的探讨和混沌分形工程应用等方面均取得了可喜的研究成果。

And we by the NDR curve of the IV curve can be observed, NDR device has a very special non-linear phenomenon, Usually composed of a non-linear circuit components are usually chaotic phenomenon, so we raise our six different structure in addition to the new frequency, and to explore the phenomenon of chaos, and the use of the cycle of chaotic phenomena in addition to the frequency multiplier effect achieved .

而我们由NDR的I-V curve曲线可以观察到，NDR元件具有非常特别的非线性现象，而通常一个非线性元件所组成的电路通常会有混沌现象，因此我们提出六种不同架构的新型除频器，并且探讨其中的混沌现象，而利用混沌现象中的周期倍增所实现除频效果。

A time-delay reconstruction of a phase space equal to the original system has been made by analyzing of observed time series of current signal and vibratory signal, and the methods of choosing properly the embedding dimension and delay-time for phase space reconstruction have been studied in detail.

本文利用振动信号和电流信号时间序列，采用时间延迟法，重构了系统的等价相空间，并详细研究了嵌入维数及时间延迟的选择对重构相空间的影响，计算了铣削加工典型过程的Lyapunov指数谱，分析了系统的混沌特性；同时采用P-G算法，计算了混沌动力系统的奇异吸引子的分维数，分析了分维数与系统状态的关系，定量地指示出系统的混沌程度，同时也反映出系统的不可预报程度。

The detail is clarified as follows: 1. First of all,the article introduce the produce and development of the chaotic theory, then meaning and the development foregrounds of study.

本文对混沌电路及其在保密通信中的应用进行了深入的研究，主要内容如下： 1、首先系统的研究了混沌理论的产生与发展，以及混沌研究的意义和发展前景。

"The earth was without form and void" Rotherham:"Now the earth had become waste and wild". It gives the idea that the earth had been created some time earlier but for some unrevealed reason had now "become without form and void".

&地是空虚混沌，&卢得汉解释&地变得空虚混沌&这暗示着地是早些时就已经创造的，只是由于一些不可知的原因变得&空虚混沌&。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。