Chaotic System Analysis And Circuit Design

The complexity of behaviors in dynamics systems is not only an important problem in circuit systems, but also a core problem in many other systems with paramount scientific significance and engineering background. Therefore, how to analyze and determine these complicated behaviors, demonstrate the dynamics mechanisms of the system, and then achieve system control has become a series of principal problems of the scientific research in recently years. Among these problems, the chaoticity verification is the hardest one, since it needs the abstruse theory of dynamical systems and topological horseshoe, a great deal of numerical computation and many works on algorithm design. In this dissertation, we study two major problems on the chaotic system, i.e. chaotic system analysis and chaotic circuit design. The main study and contributions are given as follows:1) In order to study the chaotic dynamics with one dimensional expansion, at first we provide a simple result on topological horseshoes which is very applicable for finding horseshoes with computers; then propose a method to find topological horseshoe with one dimensional expansion with this result, and the method is realized with a MATLAB GUI program; at last, we study the low dimensional Glass network and the RCLSJ(the resistive-capacitive-inductive shunted junction) model, the chaotic behaviors of the two systems are analyzed and proved by mean of topological horseshoe.2) In order to study more complicated dynamics of chaotic phenomena, i.e. chaotic behavior with more than one directional expansion, at first we propose a technique to determine topological horseshoe with multidimensional expansion by providing a simple result on topological horseshoe; then propose a method to find this kind of horseshoe with this technique, and realize it with a MATLAB GUI program; at last, we study several famous hyperchaotic systems such as the hyperchaotic Hénon map, the Rossler hyperchaotic system, the Saito Hysteresis Chaos Generator (SHCG), and the Matsumoto-Chua-Kobayashi (MCK) circuit, the hyperchaotic behaviors are analyzed and verified by mean of topological horseshoe with multidimensional expansion. Because this research is very difficult, there is no similar work in literature according the author's knowledge.3) In order to design chaotic circuits, at first we propose three methods to design a chaotic system, such as feedback switching control method, constructing topological horseshoe method, coupling subsystems method; we present many chaotic systems as examples to show these powerful method; since these system are robust in structure, we can obtain a simpler system by modifying their parameters, then we realize the simplified system with the chaotic circuits; finally, we get several chaotic circuits.In order to make a nonchaotic circuit generate chaos or get a simpler chaotic circuit, we propose three ways to chaotify the Wien bridge oscillator with the three methods mentioned above. We obtain four simple chaotic circuits. Topological horseshoes are used here to analyze and verify the chaotic and hyperchaotic dynamics.The contribution of this dissertation can make the research on chaos more reliable, and provide methods and tools for researchers to study many other chaotic systems. In addition, three new methods based on feedback switching control are also proposed to design chaotic circuits for the engineering purposes.