混沌

Based on the research results of Chaos theory, in this dissertation, it has made detailed analysis of the chaotic signal generator. Firstly, the characteristic and various detection methods of chaotic signal are recommended. Secondly, with the aid of software, such as MATLAB, PSPICE, EWB, etc, discussion of the process of generating chaotic signal proceeds. Through simulation, the output result of several kinds of chaotic circuit are analyzed and compared. Thirdly, aiming at Chuas chaotic circuit, through debugging, the impacts by components and parts in the circuit, such as operation amplifier, capacity, inductor, etc, has been further investigated. And then provides a new scheme to implement Lorenz chaotic system, the circuit design and analysis are presented in detail and it can be realized by the hardware of programmable arrays FPGA, the experimental results indicate that this scheme has the advantages of easy operation, flexible design and high efficiency. An application example in secure communications is also provided. Finally, through picking up the characteristic parameter-Lyapunov exponent of the Chaos we can analyze the performance of different chaotic signal generators.

本文在混沌理论研究成果的基础上，对混沌信号的产生做了详细的分析，涵盖以下内容：首先介绍了混沌的定义，混沌信号的基本特性和各种判别方法，特别是对简单的一维Logistic映射的硬件实现问题做了初步探索；其次对混沌信号的产生方法进行讨论，借助于MATLAB、PSPICE、EWB等仿真软件，对几种混沌电路输出的混沌信号进行了分析比较，并在此基础上针对典型三阶连续自治系统Chua's电路作进一步实验研究，通过混沌电路调试，深入研究电路中各元器件，特别是运算放大器、电容、电感等对混沌信号时域以及频谱的影响；再次研究连续混沌系统的数字化硬件产生，设计了Lorenz混沌电路在现场可编程门阵列FPGA上实现的新方案，在保密通信中的应用实验结果表明该方案具有操作简单、设计灵活、效率高等优点；最后针对不同混沌系统，采取不同算法，提取混沌特性参数Lyapunov指数，进而对不同的混沌信号发生器的性能进行了分析。

In this dissertation, firstly, the theories and methods about chaos control and chaotic optimization are studied. Based above, some new approaches for chaos control and chaotic optimization are proposed. Furthermore, the application of chaotic optimization for test generation of combinational logic circuits is investigated in detail, and new methods for test generation are proposed based on chaotic optimization.

本论文在对混沌控制与混沌优化的相关理论和方法进行较为全面、系统的研究基础上，提出了一些新的混沌控制与混沌优化方法，并针对混沌优化与混沌神经网络在组合电路测试生成问题中的应用展开了详细研究，提出了基于混沌优化的组合电路测试生成方法，得到了有价值的成果。

Chapter four (application of chaos in measurement field): In this chapter firstly the sensitivity of initial values and parameters that chaos can be used in the measurement field has been analyzed quantitatively, on this basis, the necessary conditions of chaotic system that can be used in measurement are concluded and presented; then the mechanism of measurement implemented by subsection linear map chaotic system, the coordinating relationship between chaotic output signal and the values being measured, and the precision of system measurement are further analyzed quantitatively.

第四章（混沌在测量领域中的应用）首先对混沌可用于测量领域的初值敏性和参数敏感性进行了定性分析，在此基础上，归纳并提出了可用于测量的混沌系统应具有的必要条件；定量地分析了分段线性映射混沌系统实现信号测量的基本原理、输出混沌序列与被测量间的数值对应关系及系统的测量精度等问题；并以DSP为核心设计了混沌型电压测量系统；其次提出了混沌参数敏感性用于测量的基本思路，并对此进行了计算机仿真及原理性实验电路设计。

Chapter four (application of chaos in measurement field): In this chapter firstly the sensitivity of initial values and parameters that chaos can be used in the measurement field has been analyzed quantitatively, on this basis, the necessary conditions of chaotic system that can be used in measurement are concluded and presented; then the mechanism of measurement implemented by subsection linear map chaotic system, the coordinating relationship between chaotic output signal and the values being measured , and the precision of system measurement are further analyzed quantitatively . And a chaotic voltage measurement system using DSP is designed. Secondly a basic thought that thesensitivity of chaotic parameters can be used in measurement is presented and simulated. Its theoretical testing circuits are designed.

第四章(混沌在测量领域中的应用)首先对混沌可用于测量领域的初值敏性和参数敏感性进行了定性分析，在此基础上，归纳并提出了可用于测量的混沌系统应具有的必要条件；定量地分析了分段线性映射混沌系统实现信号测量的基本原理、输出混沌序列与被测量间的数值对应关系及系统的测量精度等问题；并以DSP为核心设计了混沌型电压测量系统；其次提出了混沌参数敏感性用于测量的基本思路，并对此进行了计算机仿真及原理性实验电路设计。

Chapter three (the methods of generating chaotic signal and its applications): In this chapter firstly the mechanism that a simple kinetic system, subsection linear map system, can generate chaotic phenomena is affirmed, the characteristics of correlation function of the chaotic signal generated by this system are simulated, on this basis a simple applicable method for generating chaotic signal is given; secondly some typical circuits generating chaotic signal are designed, also use operational amplifier to design a third -order autonomous circuit with chaotic dynamics. The basic mechanism and typical structures of chaos in the application of communication are introduced systematically and a simple method is provided for generating pseudo random code signal; At last Chaotic signal is applied into the analysis of system characteristic.

第三章(混沌信号产生方法及其应用)首先针对一类简单动力学系统——分段线性映射系统能够产生混沌现象的机理及由该系统所产生的混沌信号的自协方差函数特点进行了证明和计算机仿真，提出了软件产生混沌信号的一种实用方法；其次分析讨论了几种能够产生混沌信号的典型混沌电路，提出了用运算放大器与阻容元件实现三阶自治混沌电路的基本原理；概述了混沌在通信领域中应用的基本原理和典型结构，提出了产生伪随机码信号的一种简单方法；最后将混沌信号用于系统的特性分析中。

First, the traffic flow time series chaotic feature is extracted by chaos theory. pretreatment for traffic flow time series, and the wavelet neural networks model was build by this. Second, the chaotic mechanism and the chaotic probability is described. Based on chaotic learning algorithm, and the wavelet neural networks fast learning algorithm of traffic flow time series is designed based on chaotic algorithm. Last, a single-step and multi-step prediction of traffic flow chaotic time series is researched by BP neural networks, wavelet neural networks and wavelet neural networks based on chaotic algorithm. The results showed that the wavelet neural networks predictive performance is better than the BP networks and the wavelet neural networks by the simulation results and root-mean-square value.

首先，通过混沌理论提取了交通流量时间序列的混沌特征，并在此基础上建立了小波神经网络交通流量时间序列模型；接着，阐述了混沌学习算法的混沌机理、混沌产生的概率，设计了基于混沌算法的小波神经网络交通流量混沌时间序列快速学习算法；最后利用交通流量混沌时间序列对BP网络、非混沌算法的小波神经网络以及基于混沌算法的小波神经网络进行了单步预测和多步预测，并对预测结果的仿真图和真实值与预测值的方均根进行了比较，结果表明基于混沌学习算法的小波神经网络的预测性能明显优于应用BP网络和非混沌算法的小波神经网络。

By the help of numerical analysis and graphic recognition, Duffing-van der Pol non-linear vibration system with 9 parameters has been researched, the Graphic User Interface contains initial conditions, 9 parameters, power spectrums, trochoid chart of phase portraits, Poincaré mapping, analogous dynamic graph of displacements and the analogous vibration graph of mass blocks, the various dynamic characteristics of the non-linear vibration can be attained, which makes it possible to fully implement the visualized computer experiments and study of Duffing-van der Pol non-linear vibration system.

因为混沌运动十分复杂，在研究和模拟混沌运动的过程中，不但要进行大量的数值计算，而且要将计算结果直观地展示出来以便观察混沌现象，完成这一任务非计算机不可。自从洛伦茨利用计算机发现了第一个混沌吸引子以后，30多年来正是有赖于计算机技术的发展，促使混沌的研究取得迅速的发展。另一方面，混沌运动是确定性系统中出现的一种貌似随机的现象，走向混沌有其独特的过程，只有展示出它的演化过程，才能很好地了解混沌运动。也就是说，混沌是一门关于过程、演化的科学而不是一门关于状态、存在的科学。因此，只有利用计算机才能将混沌的动态过程和演化的方式真正地体现出来。

The development and significance of chaology are introduced firstly. The general requirement of communication system and the application potential in secure communication are expatiated. The chaotic secure communication methods home and abroad are also summarized, including chaos spread spectrum communication, chaos key-shifting, chaos parameter modulation, chaos masking, chaos CDMA. The exiting problems and development direction are also pointed out respectively.

介绍了混沌学的发展过程和意义，阐述了通信系统的一般要求和混沌在保密通信中的应用潜力，综述了国内外现有的混沌保密通信方法，其中包括：混沌扩频通信，混沌键控，混沌参数调制，混沌掩盖，混沌数字码分多址等五大类，指出了各自存在的问题和发展方向。

The following exciting results are revealed: 1 When considering the influence of some nonlinear elements such as hard-limit of exciters, the effects of some devices such as Power System Stabilizer and Static Var Compensator which can introduce positive damping in power system, the reasonability of system parameter values in simulation, the SNB surface and HB surface on the boundary of SSSR will turn close to each other and even coalesce together; 2 Under some conditions, coupling between slow exciters and shunt capacitors will bring negative damping in power system dynamics, which increases the possibility of oscillatory instability. So the power system with mass shunt compensators is easily subjected to the oscillatory instability. In recent years, chaotic phenomena of power system have been reported many times. Some simulation studies even found chaos existing inside the power system SSSR. In this dissertation, chaotic phenomena in power systems are thoroughly studied in order to make clear the relation of chaos and SSSR. The following results are derived: 1 Based on Li-Yorke Theorem and their definition on the chaos, the existence of chaos in power system is verified; 2 Three possible routes of causing chaos in power system are found and deeply investigated. They are route of cascading period doubling, route of directly initial energizing and route of torus bifurcation (or quasi-periodicity). The latter two routes are investigated for the first time in power system stability studies; 3 When the stability conditions of chaos are broken, it is found they can lead to voltage collapse, angle divergence, or voltage collapse with angle divergence simultaneously.

针对在电力系统小扰动稳定区域内可能存在混沌吸引域的有关报道，本文深入研究了电力系统混沌现象的出现途径和与系统失稳模式之间的关系：1利用Li-Yorke定理和Li-Yorke的混沌定义，从理论上证明了电力系统混沌现象的存在性；2发现了电力系统中导致混沌出现的三种可能途径：倍周期分岔导致混沌、初始能量直接激发混沌和经由环面分岔导致混沌，并对后两种新发现的途径进行了较为细致的研究；3发现了混沌极限环破裂导致电压崩溃、角度失稳以及电压崩溃和角度失稳同时出现的现象，其中混沌极限环破裂导致系统角度失稳和电压崩溃及角度失稳同时出现的现象均属首次报道；4证明由微分-代数方程描述的系统模型，其小扰动稳定域的边界只包含HB、SNB和SIB三种分岔界面，在SSSR的内部和边界上，均不可能存在会导致混沌的点，从而将混沌现象排除在小扰动稳定域的研究之外，简化了后者的研究工作。

Based on the return map and the principle of closed vectors, a new method is proposed to extract unstable periodic orbits embedded in chaotic attractors. As examples, the UPOs embedded in chaotic attractors of Logistic, Hénon and Lorenz are extracted respectively by this method. And our results of Skewed Hénon map also be compared with Nusse's. These results suggest that this method is valid for unstable periodic orbits from period one to period infinite of arbitrary dimension chaotic system. The dynamic considerations of spiking and UPO coding for individual neuron and neural system under external periodic and chaotic exciting stimulus also be studied in this dissertation. A lot of spiking phenomena, such as synchronization, period, and chaos appear alternatively with the changing of the stimulus frequency. For the small stimulus frequency the neuron could completely convey the periodic signal in synchronous anti-phase into interspike intervals sequences. For the slow time–scale chaotic input, the output two ISI sequences are reciprocally related to input signals, and their oscillation wave shape in time course can be derived from that of the input signals variation, furthermore, the similar input sequence and order of UPOs, distribution of LES and value of KYD remain in attractors reconstructed from ISI sequences.

发现周期信号在单个神经元传递过程中，随着激励频率的改变，神经元输出的峰峰间期interspike interval时间序列呈现出周期、混沌和准周期的交错变化，特别当外加激励信号频率较低时，周期信号可以通过神经元ISI序列以反相同步的周期运动形式传递下去；同时无论是周期还是混沌激励信号，在神经系统中的传递均与其自身强度和神经元之间的耦合强度的大小密切相关；快变时间尺度的混沌激励信号在耦合的神经系统传递过程中，会造成大量基本信息的丢失；而慢变时间尺度的混沌激励信号在神经系统传递中，它的非线性特征信息，如混沌吸引子、不稳定周期轨道、Lyapunov指数谱和分形维数，会通过系统输出的ISI序列部分地重现出来，如与输入慢变时间尺度的混沌激励信号相比，神经系统输出的ISI序列具有：相似几何形状的混沌吸引子、相近的Lyapunov指数谱和分形维数、局部结构相同的不稳定周期轨道的排列方式。

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。