自治系统

Above method can be applied to both autonomous system and nonautonomous system.

该方法既适于自治系统又适于非自治系统。

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。

We use comparison theorem and a new method to analysis the problem of persistence and extinction.

消费者种群的长期影响，利用比较定理及一种全新的方法对自治Leslie系统给出了种群弱持续生存和灭绝的条件；对拟非自治系统给出了种群弱持续生存和灭绝的阈值。

Autonomous systems of the Internet form a huge complex network connected by physical links,in which the autonomous systems and links among them can be regarded as vertices and edges of an undirected graph.

因特网的自治系统(AutonomousSystem简称AS)构成了一个由物理链路连接起来的庞大的复杂网络，其中的自治系统及其之间的连接可以看作是无向图中的顶点和边。

The solution of some practical problems in engineering can be regarded as that of periodic solution of nonlinear autonomous systems according to the opinion of mathematics, The problems of this kind are analysed by means of the direct numerical method in this paper,The simple and convenient Draw Newton Method is applied for solving the parameter vectors in iteration course along with the calculation of a practical engineering problem.

日I崖旨J，'口工程中的一些实际问题往往可以归结为非线性自治系统，例如描述同步发电机暂态稳定性问题的转子摇摆方程，即是一典型的非线性自治系统。虽然可以用各种小参数摄动法求解非线性系统，但是这类方法是依据对线性系统的解进行"摄动"来逼近非线性系统解的。因而当系统

In this thesis, some theories and approaches related to continuous dynamics, discrete dynamics, impulsive dynamics, operator theory and numerical simulations are used to investigate dynamical behaviors including the existence and globally asymptotic stability of periodic solutions, permanence, extinction, and all kinds of complexities, and meanwhile the possible effects of delay and impulse on the dynamical behaviors are discussed.

我们的这些结果显示出这三个时滞周期系统正周期解存在且全局渐近稳定的充分条件在形式上几乎能够很好的与相应的无时滞自治系统正平衡态存在且全局渐近稳定的充分条件相对(来源：A5babBC论文网www.abclunwen.com)应，这些结果也显示了时滞对系统正周期解的存在性和全局渐近稳定性是有影响的，它们推广并改进了一些已有的相关结果。

To acquire the inherent topology properties and characteristics of the topology graph at AS-level, we introduce basic network model (Scale-free network and Small-world network) and evaluating parameters (such as cluster coefficient, average path length, degree distribution, Pearson correlation coefficient) in this thesis. Through thorough analysis of the topology of the generating topology at AS-level, we can see some apparent properties with the evaluating parameters and the inherent power-law distribution property of the derived topology. Besides, we discuss the perspective of the evolution of the networks topology based on these analyses.

为了研究Internet自治系统级拓扑的内在拓扑特性和规律，利用了复杂网络的基本网络模型(无标度网络和小世界网络)和度量参数(簇系数、平均路径长度、节点度分布、皮尔森系数等)，对生成的自治系统级拓扑进行了大量的分析，从中可以看出度量参数具有一些明显的特性，拓扑中具有一些幂律分布特性，并对网络拓扑的演化发展的趋势进行了探讨。

Chapter four studies the chaotic responses in a system consisting of simple pendulum and harmonic oscillator under bounded noise excitation. Firstly, the Melnikov function of the two-degree-of-freedom system under Hamiltonian perturbation is derived. The essential condition of the autonomous system for the probable onset of chaos is obtained, the Poincare maps of the system under small Hamiltonian perturbation and the effect of increasing perturbation on the Poincare maps are studies. Then for the non-autonomous system under damping and harmonic or bounded noise excitation, the largest Lyapunov exponent and Poincare maps are calculated. From the analysis of the largest Lyapunov exponent, the critical criterion for the onset of chaos, and the conclusion that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity parameter of Wiener process increases are obtained. The result from the analysis of Poincare maps is in agreement with that obtained from the Largest Lyapunov exponent. The effect of varying damping coefficient and intensity parameter of Wiener process is also analyzed.

第四章研究了有界噪声激励下的两自由度单摆—谐振子系统的混沌运动，首先推导了该两自由度系统仅在Hamilton扰动下的Melnikov函数，得到该自治系统可能产生混沌的必要条件；研究了该系统在小的Hamilton扰动和增大摄动情形下的Poincare截面；然后对有阻尼、谐和或有界噪声激励下的非自治系统数值计算了其最大Lyapunov指数和Poincare截面；从Lyapunov指数分析得到了这个两自由度系统产生混沌运动的临界条件及产生混沌的临界激励幅值随Wiener过程强度参数值的增大而增大的结论，Poincare截面分析的结果亦符合Lyapunov指数分析的结论；研究了Wiener过程强度参数、阻尼系数变化对Poincare截面的影响。

A simple form of the unstable manifold s for the fixed points not being on the boundary;2. Aim To study singular points, closed orbits, stable manifolds and unstable manifold s of a second order autonomous Birkhoff system.

目的研究二阶Birkhoff自治系统的奇点、闭轨、稳定流形与不稳定流形，方法用常1微分方程的定性方法进行研究，结果与结论给出二阶Birkhoff自治系统的奇点判据、闭轨判据、双曲平衡点判据，得到与其相关的平衡稳定性、稳定流形与不稳定流形等。

In Chapter 4, by means of the result obtained in Chapter 2 and as in the autonomous case, the author adopts a direct constructive method and obtains the local exact controllability for general nonautonomous first order quasilinear hyperbolic systems.

在第四章，作者以第三章建立起来的半整体C~1解理论为基础，采用一个与自治系统情况相似的直接构造方法得到了非自治一阶拟线性双曲组的局部精确能控性。

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。