混沌

People have proposed many different control method to realize the chaos synchronization. This article has conducted the thorough research to the chaotic neural network, introduced the chaos neural network synchronization method. Based on the linear matrix inequality technology and Lyapunov stability theory, we have Studied the synchronized controller design method of the global synchronization, the non-linear global synchronization and the global exponential synchronization. Here we have proposed one kind of synchronization algorithm, through which might obtain the gain matrix quickly and automatize.

本文对混沌神经网络进行了深入的研究，介绍了混沌神经网络同步方法的发展及研究现状，基于线性矩阵不等式技术和李雅普诺夫稳定性理论，分别研究了全局同步、非线性全局同步和全局指数同步的同步控制器实现方法，提出了一种实现混沌神经网络同步的算法，通过该算法可以快速得到增益矩阵的形式，实现混沌系统的同步控制，数值仿真验证了算法的有效性。

In 1990 and the pioneer works of Pecora and Carrol, The theoretical research and applied study of the chaotic control and chaotic synchronization get the development at full speed. Various kinds of methods of the chaotic control come out one after another and people find the chaotic control and chaotic synchronization can be applied to a lot of fields such as secure communications, chemical, modeling brain activity etc.

但自1990年E.Ott等人提出了OGY方法以及Pecora和Carroll关于混沌同步的开创性工作之后，混沌控制与同步的理论研究和应用研究得到飞速发展，各种控制混沌的方法相继问世，并发现了混沌控制与同步可以在诸如保密通讯、信号处理、化学反应、生态和电力系统等领域广泛应用。

Second, On the basis of analysis of density distribution of sequence points on the chaotic orbit of one-dimension chaotic mapping, a mutative interval chaotic optimization algorithm is presented in search for the solution optimums of the non-linear constrained problems with multi-variables and multi-peak values. With the objective function probability measurement approaching a limit 1, the convergence of the algorithm on the global optimal solution is proofed by aid of Chebyshev inequality.

二、基于一维混沌映射混沌点集的概率测度分析，提出了一种适于解决多变量多峰值非线性约束问题的新的混沌优化算法——变区间混沌优化算法，并应用切比雪夫不等式论证了算法依概率收敛于全局最优解。

The stochastic Bonhoeffer-Van der Pol system is first transformed into an equivalent deterministic system using the Chebyshev polynomial approximation, so that the problem of controlling stochastic chaos is reduced to the problem of controlling deterministic chaos in the equivalent system.

首先运用Chebyshev多项式逼近的方法，将随机Bonhoeffer-Van der Pol系统转化为等价的确定性系统，使原系统的随机混沌控制问题转换为等价的确定性系统的确定性混沌控制问题，继而可用Lyapunov指数指标来研究等价确定性系统的确定性混沌现象和控制问题。数值结果表明，随机Bonhoeffer-Van der Pol系统的随机混沌现象与相应的确定性Bonhoeffer-Van der Pol系统极为相似。

The major contributions of this thesis include:(1) proposing a new kind of optimal feedback control, followed by its application to chaos targeting and stabilization of high period unstable periodic orbits ;(2) stabilization of unstable fixed point in chaotic systems using some kind of nonlinear feedback control, and giving sufficient condition for the existence of the controller as well as the synthesis procedure;(3) analyzing the robustness of optimal control in chaotic Lur'e systems under the help of H〓 control theory;(4) finally and most importantly, introducing a novel method of information storage based on discrete time chaotic systems as the application of chaos control, and systematically studying different schemata for implementation, providing a theoretic basis for the design of such new kind of information storage devices with large capacity.

本文的主要工作包括，提出一种新的最优反馈控制，并将之应用于混沌引导控制及混沌系统高周期不稳定周期轨道的镇定控制；针对不动点镇定控制的一类非线性反馈控制器，文中给出该类反馈控制存在的充分条件及设计步骤；文中还利用非线性H〓鲁棒控制理论对Lur'e混沌系统中的最优线性反馈控制进行鲁棒性分析；最后，也是最重要的，作为混沌控制的应用，文中提出一种基于离散时间混沌系统的信息存储方法，系统地分析、研究了实现这种信息存储的不同方案，为以后进行这种新型大容量存储器设计提供了一定的理论依据。

Combining with the research situation in domestic and abroad, the applications of chaotic laser in the areas of communication and measurement are introduced, such as chaotic secure communication, chaotic laser ladar, and chaotic optical time domain reflectometer.

结合国内外研究现状，简要介绍了混沌激光在通信及测量领域的应用，包括混沌保密通信、混沌激光雷达和混沌光时域反射仪等技术，并指出了混沌光通信与混沌激光测距的发展趋势。

In the study of the stochastic chaos in simple pendulum, the random Melnikov process is derived and the mean-square criterion is used to determine the threshold amplitude of the bounded noise excitation for the onset of the chaos or random chaos in the system. For the coupled simple pendulum and harmonic oscillator, the Melnikov function is used to determine the condition for the onset of chaos in the case of Hamiltonian perturbations. In the case of non-Hamiltonian perturbation, the generalized random Melnikov process and mean-square criterion are used to determine the threshold amplitude of the bounded noise for the onset of random chaos.

在随机混沌研究中，应用随机Melnikov过程的均方准则研究了单摆在有界噪声激励下发生混沌或随机混沌时有界噪声激励的临界幅值；对于耦合的单摆-谐振子系统，先用Melnikov函数研究了在哈密顿扰动下发生混沌的必要条件；然后用推广的随机Melnikov过程方法研究了在非哈密顿扰动下发生随机混沌的必要条件；用最大Lyapunov指数及Poincaré截面方法结果与上述理论结果作了对比。

Secondly, the mathematical models for VE type three eccentric chaotic exciter and forrame rum oil system of chaotic vibratory roller are built. The numerical simulation and chaos identification are finished under different parameters of the exciter. The relationships between the chaotic characteristics of the exciter as well as the rame rum oil system and the parameters of the exciter are investigated.

其次，建立了& CVE—2型三偏心混沌激振器&和混沌振动压路机&机架—振动轮—土&系统的数学模型，并在激振器的不同参数条件下，对数学模型进行了数值仿真和混沌识别；研究了&混沌激振器&和&机架—振动轮—土&系统的混沌特征与激振器参数之间的关系。

These Lorenz systems are built, which are relevant and can be switched each other via the choicer. Chaotic synchronization of these systems is realized using same nonlinear feedback control method. The transmitter can be switched discretionarily among several chaotic systems, bring on ceaseless changing of the chaotic carriers in transport channel. In the receiver, the chaotic carriers are retrieved from the received signals, then the information signals are recovered.

构建了有一定关联的两个Lorenz混沌系统，并通过选择器在系统间随机切换；用同一种控制方法既能实现不同Lorenz系统的混沌同步，又能实现相同Lorenz系统的混沌同步；发送系统可以在Lorenz混沌系统间随机转换，传输信道中混沌调制信号也随之不断变化；接收系统将混沌调制信号解调后，即可获取有用信号。

To increase the security of the watermark, a new binary image encryption algorithm based on TD-ERCS map is presented. The watermark is encrypted by a chaos sequence generated by TD-ERCS map; A novel color image watermarking algorithm is proposed based on discrete chaotic map and 2-dimensions discrete wavelet transform. The watermark is encrypted by the new binary image encryption algorithm, and the encrypted watermark is embed into four sub-bands of the most deep level of blue branch of host image by three-level wavelet transform, and the embedded positions are determined by general cat cha otic map; A novel color-image blind detection watermarking algorithm is proposed based on integer wavelet transform and subsampling. The scrambled watermark is encrypted and embed into the low sub-bands after four sub-images of the Y branch of host image is transformed by two-level wavelet transform, and the embedded positions are determined by Logistic chaotic map, this watermarking scheme can realize blind extraction.

为了提高水印图像的安全性，提出了一种基于TD-ERCS混沌映射的二值水印图像的加密算法，该算法利用TD-ERCS映射产生的混沌序列加密水印图像；将离散混沌映射和二维离散小波变换相结合，研究了彩色图像水印新算法，该算法先对混沌序列加密后的水印图像进行小波变换，再嵌入到宿主图像的蓝色分量的最深层的四个子带中，嵌入位置则由广义猫映射确定；将整数小波变换和图像子采样技术应用于数字水印，提出了一种彩色图像盲提取水印算法，水印嵌入时，先对宿主图像在YIQ色彩空间中的Y分量进行子采样，并对得到的四个子图像分别进行二级离散小波变换，然后将置乱并加密后的水印图像嵌入到小波变换后的低频子带中，其嵌入位置由Logistic混沌映射产生的混沌序列确定，实现了水印的盲提取。

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。