【作者】 刘凌；

【导师】 苏燕辰；

【作者基本信息】 西南交通大学 ， 测试计量技术及仪器， 2006， 硕士

【摘要】 一般来说，非线性科学的主体包括：混沌(chaos)、分岔(bifurcation)、分形(fractal)、孤立子(solution)和复杂性(complexity)的研究。其中，混沌的研究占有极大的分量，包含着相当丰富的研究内容。文章在开始介绍了混沌的研究过程，混沌的研究手段及其在工程领域的应用前景，同时对统一的Lorenz混沌系统族的建立做了理论性阐述。在论文第三章中我们通过混沌反控制的思想与数学试探法提出了一种新的改进型Lorenz混沌系统，并主要研究了其基本动力学行为，算出Lvapunov指数、Lvapunov维数，给出了Poincare映射图以及时域图和相图；分析了系统随参数变化，平衡点变化的不同状态等。研究得出它与以往发现的混沌吸引子并不拓扑等价，但亦属于Lorenz混沌系统范畴。同时主要研究了这一新型混沌系统的基本动力学行为并对它做了详尽的理论分析，设计了它的实现电路并运用电子工作平台Electronics Workbench(EWB)软件进行了实验仿真。在确定了该混沌系统的基本特性后，本文讨论了混沌控制，介绍了当前主流的控制方法，如OGY法、自适应控制法、同步控制法等。对改进系统的控制问题，我们则采用线性反馈控制法并设计了其实现电路。论文第五章，着重研究了对改进Lorenz混沌系统的同步控制法，给出了混沌系统的自同步控制及其电路实现，研究了改进Lorenz混沌系统与另一个新的混沌系统的异结构同步控制问题；并利用自适应控制法对改进混沌系统做了分析。混沌同步控制的应用在保密通信、系统故障诊断、弱信号检测与估值等领域正逐步展开。最后一章我们初步研究了该改进混沌系统对已知信号的跟踪，这对该改进的混沌系统在混沌检测领域的进一步研究做了铺垫。更多还原

【Abstract】 Over the last four decades, chaos as a very interesting phenomenon has been intensively investigated. The phenomenon is common; it has been detected in a large number of dynamic systems of various physical natures and includes extremely abundant contents. In 1963, Lorenz found the first canonical chaotic attractor in three-dimensional autonomous system. Recently some new chaotic system has been introduced, which are all particular case of the so-called generalized Lorenz canonical form (GLCF).In the thesis, a new chaotic system which we have called a modified Lorenz system is proposed. Some basic dynamical properties, Continuous spectrum, Lyapunov exponents, fractal dimension and strange attractor of this new chaotic system are studied; the chaotic attractor obtained from this new system according to the detailed numerical as well as theoretical analysis is also the butterfly-shaped attractor which is similar to Lorenz attractor, but not equivalent chaotic attractor. And then, an electronic circuit is designed use Electronics Workbench (EWB) in order to confirm the every state and it accordance with the results of simulations.Research efforts have investigated chaos control and chaos synchronization problems in many physical chaotic systems. Nowadays, different techniques and methods have been proposed to achieve chaos control and chaos synchronization such as linear and non-linear feedback control. Based on the Lyapunov stability theory, a novel adaptive control law is derived for the synchronization of this modified Lorenz system with known and unknown system parameters. In Chapter 4, the method of chaos control which I adopt to control this new chaotic system to the equilibrium point and period is linear feedback control. In Chapter 5, chaos self-synchronization control and isomer synchronization are investigated. The two modified system which is confirmed not only by simulating but also by experimenting, similarly, two different chaotic systems which is also confirmed not only by simulating but also by experimenting.更多还原