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

这次合作研究是在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现象进行系统研究。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解的个数的一些重要性质已被阐明。找到了一种全局收敛的方法来数值识别分叉解。此外，还建立了判定推广的Libilard系统是否存在混沌的一个重要判据。2.非线性电路奇异吸引子的结构阐明了下列具有混沌特性的非线性电路：锁相环电路、扩展的Li6nard电路、某些简单的分段线性电路、神经型振荡器电路等。此外，还发展了一些分析方法来分析非线性电路中出现的奇异吸引子的普遍性质：余维二分叉理论、同宿链理论、Duffing电路的全局分叉结构理论等。3.混沌产生电路的构造阐明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产生电路的系统构造方法。4.举行公开研究会议由IEICE的非线性问题技术小组共同主办，1989年1月24日和25日在京都大学举行了一次公开研究会议。同年11月20日至21日，由NLP和中科院共同主办的第二次公开研究会议在崎玉大学举行。5.研究成果的分布IEICE工程混沌学报特刊将于1990年6月出版，由该研究小组成员编辑。在本期中，研究成果的主要部分将发表。

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.