Studies on Analysis of Generation Process of Chaos in Nonlinear Circuits and on Systematic Construction of Chaos Generation Circuits

这项合作研究是在1988年5月至1990年3月期间进行的。本研究的目的是对工程科学中的混沌问题进行系统的研究。本文的主要研究结果如下：1。非线性电路的性质关于非线性电阻电路的解的数目已经阐明了一些重要的性质。找到了一种全局收敛的分岔解数值识别方法。此外，还建立了一个检验扩展Libilard系统是否存在混沌的重要判据。2. 阐明了以下几种表现混沌的非线性电路：锁相环路电路、一种扩展的Li6nard电路、一种简单的分段线性电路、一种神经型振荡器、电路等。此外，还提出了一些分析非线性电路中奇异吸引子普遍性质的分析方法：协维二分岔理论、同斜连杆理论、Duffing电路的全局分岔结构理论等。3. 阐述了离散动力系统中混沌的详细性质。在此基础上，提出了嵌入混沌动力系统的混沌生成电路的系统构造方法。4. 由IEICE非线性问题技术小组（NLP）共同主办的开放研究会议于1989年1月24日和25日在京都大学举行。1989年11月20日和21日，在埼玉大学举行了由NLP和CAS共同主办的第二次公开研究会议。5. 由研究人员编辑的《工程混沌学报》特刊将于1990年6月出版。在这一期中，有一部分主要的研究成果即将发表。

This co-operative research has been done during the period from May, 1988 to March, 1990. The purpose of the research is to do a systematic research on chaos in engineering science. The followings are main results obtained by the research: 1. Properties of Nonlinear Circuits A number of important properties have been clarified on the numbers of solutions for nonlinear resistive circuits. A globally convergent method is found for numerically identifying bifurcating solutions. Moreover, an important criterion is established for testing the existence of chaos in an extended Libilard system. 2. Structures of Strange Attractors of Nonlinear Circuits It is clarified that the following nonlinear circuits exhibiting chaos: Phase Locked Loop Circuits, an extended Li6nard circuits, a certain simple piecewise linear circuits, a neural-type oscillator, circuit, etc.. Moreover, a number of analytical methods are developed for analyzing universal properties of strange attractors appearing in nonlinear circuits: a codimension two bifurcation theory, theory of homoclinic linkage, global bifurcation structure theory for the Duffing circuits, etc.. 3. Construction of Chaos Generation Circuits Detailed properties are clarified for chaos in discrete dynamical systems. Based on this result, systematic methods of constructing chaos generation circuits are proposed in which chaotic dynamical systems are imbedded. 4. Holding of Open Research Meetings Cosponsored by the Technical Group on Nonlinear Problems (NLP) of IEICE, an open research meeting was held on January 24 and 25, 1989 at Kyoto University. Also on November 20 and 21, 1989 second open research meeting was held at Saitama University cosponsored by NLP and CAS. 5. Distribution of Fruits of the Research The special issue of the transactions of IEICE on Engineering Chaos will be published on June, 1990, which is edited by the members of the research. In this issue, a main part of the fruits of the research is to be published.